is RaD My radar detects **Range** **and** **Domain** Watch my radar (yellow line) passing through the graph in the next slide The **DOMAIN** is the set **of** all possible x values for that **function** The **DOMAIN** is the set **of** all possible x values for that **function** What values can be substituted for x? Example The **RANGE** is the set **of** all possible y values for that **function** What values are possible/

are hyperbolas Goal: Graph simple rational **functions** Hyperbola A type **of** rational **function**. Has 1 vertical asymptote **and** 1 horizontal asymptote. Has 2 parts called branches. (blue parts) They are symmetrical. We’ll discuss 2 different forms. x=0 y=0 Hyperbola (continued) One form: Has 2 asymptotes: x = h (vert.) y = k (horiz.) Ex: Graph State the **domain** & **range**. Vertical Asymptote: x = 1 Horizontal Asymptote/

to find an Inverse ExamplesIntroduction Question How to find an Inverse ExamplesIntroduction Conclusion Next How to find an Inverse Examples You should now be able to: Calculate inverses. Calculate the **range** **and** **domain** **of** an inverse. Draw the graph **of** an inverse **function**. Introduction

**function** **Domain**: **Range**: x-intercept: 0 y-intercept: 0 Odd **function** Increasing on the interval (-∞, ∞) Cube **function** x-intercept: 0 y-intercept: 0 The **function** is neither even nor odd **Domain** & **range** nonnegative Increasing on the interval (0, ∞) Minimum value **of** 0 at x = 0 Square root fx: x-intercept: 0 y-intercept: 0 **Domain** & **range**: The **function** is odd Increasing on the interval (-∞, ∞) No local minimum or maximum Cube root fx: **Domain** **and** **range**/

. Use 1, 2, 3, **and** 4 as **domain** values. t0.5t + 1f(t)f(t) 10.5(1) + 11.5 20.5(2) + 12 30.5(3) + 12.5 40.5(4) + 13 Evaluate the **function** rule ƒ(g) = –2g + 4 to find the **range** for the **domain** {–1, 3, 5}. The **range** is {–6, –2, 6}./ ƒ(g) = –2g + 4 ƒ(5) = –2(5) + 4 ƒ(5) = –6 ƒ(g) = –2g + 4 ƒ(–1) = –2(–1) + 4 ƒ(–1) = 6 ƒ(g) = –2g + 4 ƒ(3) = –2(3) + 4 ƒ(3) = –2 Find the **range** **of** the **function** ƒ(g) = 3g – 5 for the **domain**/

Monday, Day 6 Relation – **Function** – **Domain** – **Range** – http://youtube.com/watch?v=Rj1sDWjvgjM Your team will create a “Wikipedia Entry” for an assigned astronomer. You will create your “Entry” in Word Be sure to include the following /?v=epJLSCEGjoc Take 10 Minutes 1.The Bus Departs at 8 AM, please plan to be early 2.We are meeting on “The Horseshoe”, in front **of** the building. 3.We’re going to try **and** leave GA Tech around noon so we can be back at 1 PM. 4.If you have trouble, Stephen’s Cell is: 770-597-2824 5/

more points on the graph Give the **domain** **and** **range** **of** the relation This is what you look for in a mapping diagram to determine whether or not something is a **function**. *Arrows coming from the **DOMAIN**: 2 arrows from one number Not a **function** 1 arrow from each number **Function** Give the definition **of** a **function**. A relation where each element in the **domain** is paired with exactly one element/

The definition **of** a **function** is: A **function** is a relation that maps each element in the **domain** to one **and** only one element in the **range**. What??? What is **domain**? **Domain** is the “x” values. What is **range**? **Range** is the “y” values. So a **function** in plain English is: A relation where “x” is not repeated. There are different ways to determine if a relation is a **function** depending on/

f(x) = 7x + 5 –f(x) = sin(x) **Function** Definition **Function** from A to B –written f: A B –a subset **of** A x B –A is **Domain** –B is Codomain Mapping or Transformation Equality A = A’ B = B’ F(a) = G(a) for all a A Image or **Range** –f: A B –Image is b B : f(a/,b) f for some a A Composite f(g(x)) f = 2x+3 g = 3x+5 f o g = Terms Injective (No duplicated b’s) Surjective (All b’s used) Graphs Bijective Both Injective **and** Surjective one to one correspondence /

Root **Function** Which **function** has its **domain** as the set **of** all real numbers except for 0? The Reciprocal **Function** The Reciprocal **Function** Which 2 **functions** have no negative #’s in their **domain**? The Square Root **Function** The Square Root **Function** The Natural Logarithm **Function** The Natural Logarithm **Function** Only 3 **of** the **functions** are bounded both above **and** below. Which three? The Sine **Function** The Sine **Function** The Cosine **Function** The Cosine **Function** The Logistic **Function** The Logistic **Function** Three **of**/

Relations **and** **Functions** By: Jeffrey Bivin Lake Zurich High School jeff.bivin@lz95.org Last Updated: November 14, 2007 Definitions Relation A set **of** ordered pairs. **Domain** The set **of** all inputs (x-values) **of** a relation. **Range** The set **of** all outputs (y-values) **of** a relation. Jeff Bivin -- LZHS Example 1 Relation { (-4, 3), (-1, 7), (0, 3), (2, 5)} **Domain** { -4, -1, 0, 2 } **Range** { 3, 7, 5 } Jeff/

2.1 “Relations & **Functions**” Relation: a set **of** ordered pairs. **Function**: a relation where the **domain** (“x” value) does NOT repeat. **Domain**: “x” values **Range**: “y” values Cartesian Coordinate Plane: Definitions Discrete **Function**: ordered pairs that are NOT connected. Continuous **Function**: ordered pairs that are connected in a line or a smooth curve. Vertical Line Test: used to determine if the relation is a **function**. Examples State whether the relation/

do you tell if a relation is a **function**? {(6, 3), (7, 4), (9, 3), (6, 3)} What is **domain**? What is **range**? **Domain** **and** **Range**? {(6, 3), (7, 4), (9, 3), (6, 3)} How do you evaluate a **function**? Find f(g(x)), if x = -3 f(x) = -3x + 5g(x) = x 2 – x What are roots/zeros **of** a **function**? How do you tell if your approximate/

A Day 28 Agenda: 1. Notes from a PPT: **Functions** vs. Relations / **Domain** & **Range** 2. Homework: Unit 3 Pre-Test Learning Target: Students will know what a **function** is in comparison to a relation, **and** how to determine **domain** & **range**. Standard: MCC9-12.F.IF.1 **and** 2 **Functions** vs Relations Relation Any set **of** input that has an output **Function** A relation where EACH input has exactly ONE output Each/

. MM1A1f Recognize sequences as **functions** with **domains** that are whole numbers. Sequences Sequence-a **function** whose **domain** is a set **of** consecutive whole numbers. Terms-values in the **range**. **Domain**-relative position **of** each term input **Range**-terms **of** the sequence output MM1A1f Recognize sequences as **functions** with **domains** that are whole numbers. Sequences Write terms **of** a sequence. a n = 2n-3 Find the first three terms, the **domain** **and** **range**. DomainRange a 1 = 2/

**Functions** LINEAR **AND** NON LINEAR Linear **function** What is the **function** that states that the **range** values are 2 more than the **domain** values? f(x) = x + 2 2 xf(x) = x + 2 1 02 13... Linear **function** – graph is a straight line Linear **function** What is the **function** that states that the **range** values are 1 less than twice the **domain**/ the coordinates if they are put into a table 4 Non-Linear **function** What is the **function** that states that the **range** values are the squares **of** the **domain** values? f(x) = x 2 5 x f(x)/

Inverse **Function** or Rational **Function** (Reciprocal **of** x) f(x) = 1 x Inverse **Function** or Rational **Function** (Reciprocal **of** x) Parent Equation: **Domain**: **Range**: f(x) = 1 x Inverse **Function** or Rational **Function** (Reciprocal **of** x) Parent Equation: x – intercept: y – intercept: Inverse **Function** or Rational **Function** (Reciprocal **of** x) Table: xy -2-0.5 0Error 11 20.5 f(x) = 1 x Parent Equation: Graph Description: Opposite “L” Curves in 1 st **and** 3/

**Functions** as graphs Working with **functions** Intro Question... **Functions** Mappings **Functions** as graphs Working with **functions** Intro What kind **of** mapping is this? One-to-0neOne-to-manyMany-to-one Conclusion **Functions** Mappings **Functions** as graphs Working with **functions** Next Intro You should now be able to: Find the **range** **and** **domain** **of** a mapping. Categorise mappings (one-to-one, etc.) Do simple computations with **functions**. When you feel comfortable move on to composition **of** **functions**/

every x there is exactly one y. **Domain** - set **of** x-values **Range** - set **of** y-values Open books to page 40, example 1. Tell whether the equations represent y as a **function** **of** x. a.x 2 + y = 1Solve for y. y = 1 – x 2 For every number we plug in for x, do we get more than / the **domain** **of** each **function**. a.f: {(-3,0), (-1,4), (0,2), (2,2), (4,-1)} **Domain** = { -3, -1, 0, 2, 4} b. D: c. Set 4 – x 2 greater than or = to 0, then factor, find C.N.’s **and** test each interval. D:[-2, 2] Ex.g(x) = -x 2 + 4x + 1 Find:a.g(2) /

f (x) = x 2 + 5, find f (3) = f (-8) = f (5280) = f (r) = f (w) = f (BOB) = f (2x – 3) = Composition **of** **functions** (a more nerdy version **of** inception) means we take the equation for g(x) **and** plug that into f(x). (f composed with g) frac{f(x)}{g(x)} f( **Domain**: **Range**: **Domain**: **Range**: frac{f(x)}{g(x)} f( **Domain**: **Range**: **Domain**: **Range**: Try. Quiz next Class

–4 –2 1 Y X Answer: This relation is not a **function** because the element 3 in the **domain** is paired with both 2 **and** –1 in the **range**. Answer: This is a **function** because the mapping shows each element **of** the **domain** paired with exactly one member **of** the **range**. Example 6-1d Algebra 4-6 **Functions** **Functions** You can use the vertical line test to see if a graph/

this piecewise **function**? Explain. Graphing by tables Writing equations **of** lines xf(x)f(x)xf(x)f(x) Writing an equation **of** a line If you have slope **and** y-intercept: If you have slope **and** a point:/**Functions** A _________ **function** is a piecewise **function** that consists **of** different constant **range** values for different intervals **of** the **function**’s **domain**. 1 -2-3 2 -3 -2 3 1 3 2 Rounding-down **function** Greatest integer **function** 28.Graph the step **function**. 29.What is the **domain**? 30.What is the **range**? 31.Why is the **range**/

the graphs **of** f(x) = sin x **and** f -1 (x) = arcsinx 5.Find the values **of** (f -1 )’(a) if given f(X)=sinx where a= 6.Draw the tangent line to (f -1 )(a) at a= **Domain**: **Range**: **Function**: y = arcsinxThe derivative formula: Graph: **Domain**: **Range**: **Function**: y = arctanx Graph: **Domain**: **Range**: **Function**: y = arcsecx Graph: The derivative formula: Inverse Trig **Functions** **and** Derivatives **Domain**: **Range**: **Function**: y = arccosx Graph: **Domain**: **Range**: **Function**: y = arccotx Graph: **Domain**: **Range**: **Function**: y = arccscx/

), h(0) h(-3) = h(0) = Give the **domain** **and** the **range** **of** these **functions**. **Domain**: **Range**: **Domain**: **Range**: Give the **domain** **and** the **range** **of** these **functions**. **Domain**: **Range**: **Domain**: **Range**: 12341234 0 InputOutput 10 20 30 40 50 100 200 300 400 500 Input Output What is the **domain** **and** **range** **of** this table? **Domain**: **Range**: Given the **function** f(x) = 2x + 5 Find the **domain** **and** the **range** **of** the data InputOutput 3 4 5 6 7 **Domain**: **Range**: 12341234 Set ASet B abcdabcd Set ASet B 12341234/

: Y-intercepts: Roots (x-int): VA: HA: **Domain**: **Range**: Example: **Example: Transformations: VA: HA: **Domain**: **Range**: What is the **domain** for f(x) ≥ -7? Y-intercepts: Roots (x-int): VA: HA: **Domain**: **Range**: Rational Parent **Function** Rational Standard Form Example:Example: Transformations: VA: HA: **Domain**: **Range**: Y-intercepts: Roots (x-int): VA: HA: **Domain**: **Range**: Transformations: VA: HA: **Domain**: **Range**: *Go to calculator to graph **and** get idea **of** lines between asymptotes – watch out for parenthesis/

- 2 Example 1 DETERMINING INTERVALS **OF** CONTINUTIY Describe the intervals **of** continuity for each **function**. Solution The **function** is continuous over its entire **domain**,(– , ). 2.6 - 3 Example 1 DETERMINING INTERVALS **OF** CONTINUTIY Describe the intervals **of** continuity for each **function**. Solution The **function** has a point **of** discontinuity at x = 3. Thus, it is continuous over the intervals, (– , 3) **and** (3, ). 3 2.6 - 4 **Domain**: (– , ) **Range**: (– , ) IDENTITY **FUNCTION** (x) = x xy – 2/

**Functions** The exponential **function** is a **function** **of** the form a >0, a ≠ 1 In the definition **of** an exponential **function**, a, the base, is required to be positive. **Domain**: **Range**: Theorem Example Solution (i) Evaluate the limit (ii) Sketch the graph **of** the **function** The Natural Exponential **Function** The value **of** e accurate to eight places is 2.71828183. Basic Properties **of** Natural Exponential **Function** 3- Hyperbolic **Functions** The hyperbolic **functions** are some combinations **of** **and** arise/

$20. How many pounds was Kim’s pumpkin? Equation Y=.25 or F(x)=.25 Independent **and** Dependent Variables Independent- number **of** pounds Dependent- cost Is this a **function**?? Yes it’s a **function** because the x values don’t repeat. **Domain** **and** **Range** **Domain**- The x values (0,1,2,3,4) **Range**- The y values (0,.25,.50,.75,1) Continuous or Discrete? It’s continuous because/

out this machine! Input Output November 2001 Created by Cathy Stevens7 Think **of** a relation in terms **of** input **and** output Input, x 035035 -2 1 5 6 Output, y November 2001 Created by Cathy Stevens8 The Vocabulary **of** Relations X Input **Domain** **Range** Output y November 2001Created by Cathy Stevens 9 A **function** is a relation in which no two ordered pairs have the same x/

, we can’t input negative numbers into our **function**. The output, again, can only be positive. ? ? Sketch: ? **Function** **Domain** **Range** **Function** **Domain** **Range** Mini-Exercise In pairs, work out the **domain** **and** **range** **of** each **function**. A sketch may help with each one. **Function** **Domain** **Range** **Function** **Domain** **Range** **Function** **Domain** **Range** 1 2 3 **Function** **Domain** **Range** 4 **Function** **Domain** **Range** **Function** **Domain** **Range** 8 9 ? ? ? ? ? ? ? 5 **Function** **Domain** **Range** ? 6 7 ? **Range** **of** Quadratics A common exam question is to determine the/

for general purpose contrast manipulation Transformations Piecewise Linear Transformations Transformations Thresholding **Function** g(x,y) =L if f(x,y) > t, 0 else t = ‘threshold level’ Piecewise Linear Transformations Input gray level Output gray level Gray Level Slicing Purpose: Highlight a specific **range** **of** grayvalues Two approaches: 1. Display high value for **range** **of** interest, low value else (‘discard background’) 2. Display high value for/

Value **Function** The Reciprocal **Function** The Reciprocal **Function** The Squaring **Function** The Squaring **Function** Which three **functions** have NO zeros? The Reciprocal **Function** The Reciprocal **Function** The Exponential **Function** The Exponential **Function** The Logisitic **Function** The Logisitic **Function** Which 3 **functions** have a **range** **of** ? Which 3 **functions** have a **range** **of** ? The Identity **Function** The Identity **Function** The Natural Logarithm **Function** The Natural Logarithm **Function** The Cubing **Function** The Cubing **Function** Which/

2 2 2 4 3 6 4 8 Not a **function**, the red line passes through 2 points during the vertical line test. 2 4 2 4 -2 -4 -2-4 6 8 -6 -8 -6-8 68 **Domain** **Range** Input Output Open PW to page 11 **and** complete problems 3, 4, **and** 5 One **of** four parts into which the axes divide a coordinate plane/

**AND** DECAY? Identify which **functions** represent GROWTH **and** which ones represent DECAY RATE YOUR LEVEL **OF** UNDERSTANDING Got it! Almost There! HELP!!! MAIN QUESTION DISCOVERY **Domain**: All Real Numbers HOW DO I GRAPH WITH AN EXPONENTIAL **FUNCTION**? Example 1 **Domain**: **Range**: HOW DO I GRAPH WITH AN EXPONENTIAL **FUNCTION**? Example 2 **Domain**: **Range**: HOW DO I GRAPH WITH AN EXPONENTIAL **FUNCTION**? Example 3 **Domain**: **Range**: HOW DO I GRAPH WITH AN EXPONENTIAL **FUNCTION**? Example 4 **Domain**: **Range**/

-world problems Today’s Objective: I can graph a rational **function**. Rational **Function**: Hole Asymptote Continuous Graph: No breaks in graph Discontinuous Graph: Breaks in graph V. Asymp: Holes: **Domain**: Discontinuity: Vertical Asymptotes: Non-removable Discontinuities: Holes: Removable Same factor in numerator **and** denominator **Domain**: Where the Denominator = zero Horizontal Asymptotes: No horizontal asymptote Leading term **of** numerator **and** denominator (standard form) No horizontal asymptote 1.Find/

the graph **of** a rational **function** can sometimes cross a horizontal asymptote. However, the graph will approach the asymptote when |x| is large. Holt McDougal Algebra 2 Rational **Functions** Holt McDougal Algebra 2 Rational **Functions** HA: VA: Graph the **function** (p < q). State the **domain** **and** **range**. x-intercepts: xy xy **Domain**: **Range**: Holt McDougal Algebra 2 Rational **Functions** HA: VA: Graph the **function** (p < q). State the **domain** **and** **range**. zeros: xy xy **Domain**: **Range**: Holt/

. 2 Main Paths –Math/Science/Engineering (Alg3 or Precalculus) –Business (AP Stats or PAP Stats) Square Root **Functions** Objectives I can graph square root **functions** using transformations without a calculator I can determine the equation **of** a square root **function** from its graph. I can determine **domain** **and** **range** in Interval Notation from a graph Square Root What are critical points Xy 0 1 4 9 16/

7/3/2013 **Domain**: Set **of** Inputs ◦ Found on the x-axis **Range**: Set **of** Outputs ◦ Found on the y-axis **Domain** Set-Builder Notation Interval Notation **Range** Set-Builder Notation Interval Notation What is **domain**? What is **range**? What is an intercept (both x **and** y)? P. 212 #77-92 The figure below shows the percent distribution **of** divorces in the U.S. by number **of** years **of** marriage. YES! Your temperature/

1.5 Library **of** **Functions** Classify **functions** **and** their graphs Linear **Functions** (a line) **Domain**: All Realsy = mx + b **Range** : All RealsAx + By + C = 0 Y intercept (0, b) Writing a linear **function** Let f(2) = 5; f(4) = 7Points (2, 5);(4, 7) Find the slope y – 5 = 1(x – 2) Writing a linear **function** Let f(2) = 5; f(4) = 7Points (2, 5);(4, 7) Find the slope/

**of** a quadratic **function**? Vertex: (1, 7) o y-value is called maximum o Parabola opens downward (a < 0) Finding **domain** & **range** **Domain**: ALWAYS all real # **Range**: ALWAYS an inequality –y coordinate **of** vertex represents minimum or maximum value **of** **range** **Range**: y ≥ -6 Finding **domain** & **range** **Domain**: all real # **Range**: y ≤ 7 What is the axis **of**/1 **and** x = 2 What are the zeros **of** a quadratic **function**? one real zero o x = 1 What are the zeros **of** a quadratic **function**? No real zeros Determining a **Function** /

a negative number, the steps go downward instead **of** upwards, but the rules for step length **and** distance between steps still apply Examples Constant **Function** **Domain** is all real numbers **Range** is b from f(x)=b Examples Identity **Function** Identity **Function** y=x **Domain** is all real numbers **Range** is all real numbers Absolute Value **Function** **Domain** is all real numbers **Range** depends on equation Changes that can be made to/

some different features about the graph that are unique from previous **functions** we have graphed. x-4-20124 y Rational **Functions**: Graphs Review **Domain** **and** **Range** **Domain**: x values, input **Range**: y values, output Vertical asymptote is a value excluded from the **domain** Horizontal asymptote is a value excluded from the **range** Find the **domain** **and** **range** **of** the **functions** Find the **domain** **and** **range** **of** the **function** Graphing: Find all asymptotes – Vertical: Denominator = 0 – Horizontal: If only an/

earnings after 4 weeks. Input (# **of** weeks) **Function** rule ( x 5) Output (total earnings) 1 5 x 1 5 2 5 x 2 10 3 5 x 3 15 4 5 x 4 20 Words to Know **Domain**= the input values **Range**= the output values In our example the **domain** would be written as { 1, 2, 3, 4 } **and** the **range** would be written as { 5, 10/

~adapted from Walch Education **Domain** **and** **Range** ~adapted from Walch Education Concepts: The **domain** is the set **of** x-values that are valid for the **function**. The **range** is the set **of** y-values that are valid for the **function**. A **function** maps elements from the **domain** **of** the **function** to the **range** **of** the **function**. Each x in the **domain** **of** a **function** can be mapped to one f(x) in the **range** only. More… To create a mapping, list/

Graphs **of** Exponential **and** Logarithmic **Functions** Graph **of** Exponential **Function** f ( x ) = bx **Domain**: ( −∞, ∞ ) or x ∊ ℝ **Range**: ( 0, ∞ ) or y > 0 Intercept: ( 0, 1 ) y -intercept Asymptote: y = 0 Horizontal Graph **of** Exponential **Function** f ( x ) = 2x **Domain**: ( −∞, ∞ ) or x ∊ ℝ **Range**: ( 0, ∞ ) or y > 0 Intercept: ( 0, 1 ) Asymptote: y = 0 Now, graph: g ( x ) = 2(x – 3) + 4 **Domain**: ( −∞, ∞ ) or x ∊ ℝ No change **Range**: ( 4, ∞ ) or y > 4 Up by 4 Intercept: ( 0/

1 }. 3 Graph : for each real x, the real sin (x) [-1,1]. Formally, the graph **of** a **function** can be thought **of** as a set **of** pairs : { (x,y) ( Reals [-1,1] ) | y = sin ( x ) } = { …, (0,0), …, ( /2, 1), …, ( ,0), …, (3 /2,-1), … }. 1 0 If **domain** **and** **range** **of** a **function** are finite, then the graph can be given by a table : true true true true false/

equation. Match a graph to its equation. Determine the **domain**, **range**, asymptotes, period **and** phase shift **of** the graph **of** a tangent, cotangent, secant, or cosecant **function** given a graph. Draw the graphs **of** a tangent, cotangent, secant, or cosecant **function**. Determine if the sine, cosine, tangent, cotangent, secant, or cosecant **functions** are even, odd, or neither. General **Function** Graph the **function** tan(x) on the interval [―2π, 2π] What is/

inverse trig **functions** for specific **domains** **and** **ranges** Evaluated inverse trig **functions** Evaluated compositions **of** trig **functions** 2 **Functions** that are inverses 2 **Functions** that are not inverses by evaluating the inner most **function** first 2 **Functions** that are not inverses by drawing a triangle Sine **Function** 1 - 𝜋 2 𝜋 2 -1 Cosine **Function** 1 π 𝜋 2 -1 Tangent **Function** - 𝜋 2 𝜋 2 Evaluating Inverse Trig **Functions** arcTan (- 3 ) Cos −1 (− 3 2 ) arcSin (-1) Composition **of** **Functions** When the/

TO … Find the **domain** **and** **range** **of** a **function** given its graph Perform operations on **functions** (add, subtract, multiply, divide) Compose two **functions** Find **and** verify inverses Graph absolute value **functions** Solve absolute value equations **and** inequalities D OMAIN **AND** R ANGE F IND THE **DOMAIN** F IND THE **DOMAIN** **AND** **RANGE** F UNCTION O / X ) = X ²+ 1 G ( X ) = X – 5 Find g(f(x)) I NVERSE F UNCTIONS V ERIFY THAT THE TWO **FUNCTIONS** ARE INVERSES F(x) = 0.5x + 4 F -1 (x) = 2x – 8 F IND THE INVERSE F UNCTION y = x 2 /

graph at the right. Prerequisite Skills SKILL CHECK Graph the **function**. State the **domain** **and** **range**. ANSWER 4. y = –2 x – 1 5. y = x + 3 6. y = x – 2 + 5 3 **domain**: x > 0, **range**: y < 1 **domain**: x > 3, **range**: y > 0 **domain**: all real numbers, **range**: all real numbers Prerequisite Skills SKILL CHECK Find the inverse **of** the **function**. 7. y = 3x + 5 8. y = –2x 3 + 1 9/

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