Create a table and Graph:. Reflect: Continued x-intercept: y-intercept: Asymptotes: xy -31/3 -21/2 1 -1/22 xy 1/2-2 1 2-1/2 3-1/3.

Slides:

Advertisements

Similar presentations

Write equation or Describe Transformation. Write the effect on the graph of the parent function down 1 unit1 2 3 Stretch by a factor of 2 right 1 unit.

Advertisements

Graph of Exponential Functions

Section 2.5 Transformations of Functions. Overview In this section we study how certain transformations of a function affect its graph. We will specifically.

State the domain and range of each function. 3.1 Graphs of Exponential Functions.

3.1 – Paired Data and The Rectangular Coordinate System

Basic Functions and Their Graphs

Lesson 5-8 Graphing Absolute Value Functions

Transforming reciprocal functions. DO NOW Assignment #59  Pg. 503, #11-17 odd.

Reciprocal Graphs Sketch and hence find the reciprocal graph y = 0 y = 1 y = 2 y = 1/2 y = 3 y = 1/3 x = 1 y = 0 Hyperbola Asymptote Domain: x  R\{1}

GRAPHING RATIONAL FUNCTIONS ADV122. GRAPHING RATIONAL FUNCTIONS ADV122 We have graphed several functions, now we are adding one more to the list! Graphing.

Exponential Growth and Decay Functions. What is an exponential function? An exponential function has the form: y = ab x Where a is NOT equal to 0 and.

Exponential Functions Section 1. Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

3.2 Graphing Functions and Relations

Aim: What is an exponential function?

2 x = 42 y = 82 z = 6 X = 2y = 3 Z = ? Mathematicians use a LOGARITHM to find z and we will study logarithmic functions this unit A logarithm is the inverse.

Warm Up Graph the function

Exponential Functions Section 1. Exponential Function f(x) = a x, a > 0, a ≠ 1 The base is a constant and the exponent is a variable, unlike a power function.

Graphing absolute value functions and transformations

Find the x and y intercepts of each graph. Then write the equation of the line. x-intercept: y-intercept: Slope: Equation:

2.7 Graphing Absolute Value Functions The absolute value function always makes a ‘V’ shape graph.

Mrs. McConaughyHonors Algebra 21 Graphing Logarithmic Functions During this lesson, you will:  Write an equation for the inverse of an exponential or.

Graphing Test Review Algebra. Express the relation as a set of ordered pairs and the inverse. xy

Asymptote. A line that the graph of a curve approaches but never intersects. Add these lines to your graphs!

For the function determine the following, if it exists. 1.Vertical asymptotes 2.Horizontal asymptotes 3.Oblique asymptotes 4.x-intercepts 5.y-intercept.

Graphing Reciprocal Functions

What is the symmetry? f(x)= x 3 –x.

(7.1 & 7.2) NOTES- Exponential Growth and Decay. Definition: Consider the exponential function: if 0 < a < 1: exponential decay if a > 1: exponential.

6.3 Logarithmic Functions. Change exponential expression into an equivalent logarithmic expression. Change logarithmic expression into an equivalent.

6.2 Exponential Functions. An exponential function is a function of the form where a is a positive real number (a > 0) and. The domain of f is the set.

State the domain and range of each function Exponential Growth and Decay.

8-2 Properties of Exponential Functions. The function f(x) = b x is the parent of a family of exponential functions for each value of b. The factor a.

Exponential GrowthExponential Decay (0,a) Exponential Parent Fcn: Growth: b > 1 Decay: 0 < b < 1 H.Asymptote: y = 0 y-int is a_(1 on parent fcn) Shifts:

Equations of Lines Standard Form: Slope Intercept Form: where m is the slope and b is the y-intercept.

Graphs & Models (Precalculus Review 1) September 8th, 2015.

Translations Translations and Getting Ready for Reflections by Graphing Horizontal and Vertical Lines.

4.3 – Logarithmic functions

Exponential Functions Exponential Growth Exponential Decay y x.

Graphing Exponential function parent function: y = 2 x X is the exponent!!! What does this look like on a graph? In the parent function the horizontal.

Square Root Function Graphs Do You remember the parent function? D: [0, ∞) R: [0, ∞) What causes the square root graph to transform? a > 1 stretches vertically,

Rational Functions Essential Questions

 A function that can be expressed in the form and is positive, is called an Exponential Function.  Exponential Functions with positive values of x are.

8.2 Transformations of Logarithmic Functions

(a) (b) (c) (d) Warm Up: Show YOUR work!. Warm Up.

Unit 3. Day 10 Practice Graph Using Intercepts.  Find the x-intercept and the y-intercept of the graph of the equation. x + 3y = 15 Question 1:

Warm Up for Lesson 3.5 1)Solve: x 2 – 8x – 20 = 0 2) Sketch the graph of the equation y = 2x – 4.

5.8 Graphing Absolute Value Functions I can graph an absolute value function and translate the graph of an absolute value function.

Notes Over 4.2 Sketching Graphs of a Rational Function Steps in Graphing a Rational Function. 1.Find the vertical and horizontal asymptotes of the function.

EXAMPLE 1 Compare graph of y = with graph of y = a x 1 x 1 3x3x b. The graph of y = is a vertical shrink of the graph of. x y = 1 = y 1 x a. The graph.

Exponential Function. 1. Investigate the effect of a =+/-1 on the graph : 2. Investigate the effect of a on the graph: 3. Investigate the effect of q.

Math – Exponential Functions

The base e P 667. Essential Question How is the graph of g(x) = ae x – h + k related to the graph of f(x) = e x.

Notes Over 9.2 Graphing a Rational Function The graph of a has the following characteristics. Horizontal asymptotes: center: Then plot 2 points to the.

Today in Pre-Calculus No calculators needed Notes: –Rational Functions and Equations –Transformations of the reciprocal function Go over quiz Homework.

Twenty Questions Rational Functions Twenty Questions

Holt Geometry 3-1 Lines and Angles A-CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on.

Graphs of Exponential Functions. Exponential Function Where base (b), b > 0, b  1, and x is any real number.

Section 10.1 Day 1 Square Root Functions Algebra 1.

Algebra 2 Notes May 20, Homework #63 Answers 1) 4) 7) direct; 8) inverse; 12) neither 13) 17) A varies jointly with b and h 18) h varies directly.

Section 6.2 – Graphs of Exponential Functions

Rational Functions and Their Graphs

Chapter 4: Rational, Power, and Root Functions

Graphing Exponential Functions

Attributes and Transformations of Reciprocal Functions

2.7 Graphing Absolute Value Functions

Rational Functions Essential Questions

2.7 Graphing Absolute Value Functions

Section 10.1 Day 1 Square Root Functions

LEARNING GOALS FOR LESSON 2.6 Stretches/Compressions

PARENT GRAPH TOOLKIT Name: Lines x y x y x y

Presentation transcript:

Create a table and Graph:

Reflect: Continued x-intercept: y-intercept: Asymptotes: xy -31/3 -21/2 1 -1/22 xy 1/ /2 3-1/3

1.2.

Learning Target  I can graph a reciprocal function, and transform it  I can translate a reciprocal function, up and down, right and left. Success Criteria

Horizontal Shift:  Graph by making tables. State the domain and range.  Key: You need several positive and negative x- values to complete your graph xy -4-1/3 -3-1/2 -2 ERR 01 11/2 21/3

Horizontal Shift: Continued x-intercept: y-intercept: Asymptotes:

Vertical Shift:  Graph by making tables. State the domain and range.  Key: You need several positive and negative x- values to complete your graph xy -21/2 1 -1/20 0ERR 1/ /2

Vertical Shift: Continued x-intercept: y-intercept: Asymptotes:

DO NOW

Coming up with equation from asymptotes