Rational Functions Characteristics. What do you know about the polynomial f(x) = x + 1?

Slides:

Advertisements

Similar presentations

4.4 Rational Root Theorem.

Advertisements

Section 7.3 Power Functions and Functions Operations.

Composite Functions. Objectives  Add, subtract, multiply, and divide functions.  Find compositions of one function with another function.

Functions Basic Concepts Value (Image), Domain, Range, Graph.

Relations and functions

EXAMPLE 4 Graph a translated square root function Graph y = –2 x – Then state the domain and range. SOLUTION STEP 1 Sketch the graph of y = –2 x.

Rational Functions Find the Domain of a function

2.7 – Graphs of Rational Functions. By then end of today you will learn about……. Rational Functions Transformations of the Reciprocal function Limits.

3.7 Graphs of Rational Functions

(1) What is the slope of the line through (2,3) and (5,-9)? A. 2 B. 0 C.-4 D.-1.

1.7 Combination of Functions

Limit Laws Suppose that c is a constant and the limits lim f(x) and lim g(x) exist. Then x -> a Calculating Limits Using the Limit Laws.

Unit 6 GA2 Test Review. Find the indicated real n th root ( s ) of a. a. n = 3, a = –216 b. n = 4, a = 81 SOLUTION b. Because n = 4 is even and a = 81.

Section Functions Function: A function is a correspondence between a first set, called the domain and a second set called the range such that each.

POLYNOMIAL, RATIONAL, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS College Algebra.

AAT SEMESTER 2 REVIEW Lets Get Rich. Polynomials Find the zeroes of the polynomial f(x)= with a given factor (x-3)

7.6 Rational Zero Theorem Algebra II w/ trig. RATIONAL ZERO THEOREM: If a polynomial has integer coefficients, then the possible rational zeros must be.

Pg. 149 Homework Pg. 149#2 – 23 (every 3 rd problem) Pg. 151# #1[-5, 5] by [-2, 10] #4[-4, 4] by [-10, 10] #7[-1,000, 3,000] by [-15,000,000, 2,000,000]

ACTIVITY 35: Rational Functions (Section 4.5, pp )

Chapter 7 7.6: Function Operations. Function Operations.

Operations on Functions Lesson 3.5. Sums and Differences of Functions If f(x) = 3x + 7 and g(x) = x 2 – 5 then, h(x) = f(x) + g(x) = 3x (x 2 – 5)

ACTIVITY 31: Dividing Polynomials (Section 4.2, pp )

Theorems About Roots of Polynomial Equations. Find all zeros: f(x)= x +x –x Synthetic Division one zero…need 2 more use (x – k), where.

Chapter 4: Polynomial and Rational Functions. Warm Up: List the possible rational roots of the equation. g(x) = 3x x 3 – 7x 2 – 64x – The.

Solving equations with polynomials – part 2. n² -7n -30 = 0 ( )( )n n 1 · 30 2 · 15 3 · 10 5 · n + 3 = 0 n – 10 = n = -3n = 10 =

Alg 2 Unit 1 Review Whiteboard- Partner Work. State the Domain and Range using Set Notation Does the graph represent a function? State the interval of.

4.4 The Rational Root Theorem

Chapter 4: Polynomial and Rational Functions. Determine the roots of the polynomial 4-4 The Rational Root Theorem x 2 + 2x – 8 = 0.

Jeopardy Factoring Functions Laws of Exponents Polynomial Equations Q $100 Q $200 Q $300 Q $400 Q $100 Q $200 Q $300 Q $400 Final Jeopardy Q $500.

Solving Polynomials.

State the Domain and Range. 3  /2  /2  22 –1 1 -- -2  -3  /2-  /2.

2.6. A rational function is of the form f(x) = where N(x) and D(x) are polynomials and D(x) is NOT the zero polynomial. The domain of the rational function.

6.6 Function Operations Honors. Operations on Functions Addition: h(x) = f(x) + g(x) Subtraction: h(x) = f(x) – g(x) Multiplication: h(x) = f(x) g(x)

Polynomial Long Division

Last Answer LETTER I h(x) = 3x 4 – 8x Last Answer LETTER R Without graphing, solve this polynomial: y = x 3 – 12x x.

1. Function or Not a Function? 2. Write the closed (explicit) model of the sequence: 3, 7, 11, 15, 19.

Parent Functions. Learning Goal I will be able to recognize parent functions, graphs, and their characteristics.

GRAPHING RATIONAL FUNCTIONS

Calculus section 1.1 – 1.4 Review algebraic concepts

Real Zeros Intro - Chapter 4.2.

Finding Real Roots of Polynomial Equations

2.2 Polynomial Function of Higher Degrees

IF c is constant and lim f(x) and lim g(x) exist then…

Chapter 7 Functions and Graphs.

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Homework Questions.

Graphing Polynomial Functions

2.7 Graphs of Rational Functions

Objective 1A f(x) = 2x + 3 What is the Range of the function

Rational Functions, Transformations

Parent Functions.

Warm Up Graph the following y= x4 (x + 3)2 (x – 4)5 (x – 3)

Parent Functions.

Homework Questions.

Composition OF Functions.

2.6 Operations on Functions

Composition OF Functions.

Warm Up Use long division to find (6

SQUARE ROOT Functions 4/6/2019 4:09 PM 8-7: Square Root Graphs.

Chapter 3 Graphs and Functions.

2.7 Graphs of Rational Functions

Characteristics.

8-5 Rational Zero Theorem

Warm-up: CW: Cumulative Review 5 F(x) = 2x3 + 3x2 – 11x – 6

Characteristics.

Chapter 3 Graphs and Functions.

Warm up Write the equation in vertex form of the quadratic equation that has been: 1. shifted right 7 and down reflected across the x-axis and shifted.

Preview to 6.7: Graphs of Polynomial

Review for Test #1 Calculus – Larson.

Presentation transcript:

Rational Functions Characteristics

What do you know about the polynomial f(x) = x + 1?

What is the Domain? How do you determine the Domain? What is the Range? How do you determine the Range?

Where are the Roots or Zeros found? What are some different ways you know to find them? What is the End Behavior? How do you know?

What do you know about the polynomial g(x) = x 2 + 3x – 10?

What is the Domain? How do you determine the Domain? What is the Range? How do you determine the Range?

Where are the Roots or Zeros found? What are some different ways you know to find them? What is the End Behavior? How do you know?

Now let’s consider the case of the rational function r(x) = where f and g are the polynomial functions as shown before.

What is the Domain? How do you determine the Domain? What is the Range? How do you determine the Range?

Where are the Roots or Zeros found? What are some different ways you know to find them? What is the End Behavior? How do you know?

What do you know about the rational equation r(x) = f(x)/g(x) if f(x) = 5 and g(x) = x 2 – 6x +8?

What is the Domain? How do you determine the Domain? What is the Range? How do you determine the Range?

Where are the Roots or Zeros found? What are some different ways you know to find them? What is the End Behavior? How do you know?

What do you know about the rational equation r(x) = 2x 2 + 7x – 4 ? x 3 – 1

What is the Domain? How do you determine the Domain? What is the Range? How do you determine the Range?

Where are the Roots or Zeros found? What are some different ways you know to find them? What is the End Behavior? How do you know?