Presentation is loading. Please wait.

Presentation is loading. Please wait.

Chapter 1 Functions and Their Graphs. Warm Up 1.4 A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window.

Similar presentations


Presentation on theme: "Chapter 1 Functions and Their Graphs. Warm Up 1.4 A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window."— Presentation transcript:

1 Chapter 1 Functions and Their Graphs

2 Warm Up 1.4 A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window if the total area of the square and the semicircle is to be 200 ft 2. 2 x x

3 1.4 Transformation of Functions Objectives:  Recognize graphs of common functions.  Use vertical and horizontal shifts and reflections to graph functions.  Use nonrigid transformations to graph functions. 3

4 Vocabulary Constant Function Identity Function Absolute Value Function Square Root Function Quadratic Function Cubic Function Transformations of Graphs Vertical and Horizontal Shifts Reflection Vertical and Horizontal Stretches & Shrinks 4

5 Common Functions Sketch graphs of the following functions: 1. Constant Function 2. Identity Function 3. Absolute Value Function 4. Square Root Function 5. Quadratic Function 6. Cubic Function 5

6 Constant Function 6

7 7 Identity Function

8 Absolute Value Function 8

9 Square Root Function 9

10 Quadratic Function 10

11 Cubic Function 11

12 Exploration 1 Graph the following functions in the same viewing window: y = x 2 + c, where c = –2, 0, 2, and 4. Describe the effect that c has on the graph. 12

13 Exploration 2 Graph the following functions in the same viewing window: y = (x + c) 2, where c = –2, 0, 2, and 4. Describe the effect that c has on the graph. 13

14 Vertical and Horizontal Shifts Let c be a positive real number. Shifts in the graph of y = f (x) are as follows: 1. h(x) = f (x) + c ______________________ 2. h(x) = f (x) – c ______________________ 3. h(x) = f (x – c) ______________________ 4. h(x) = f (x + c) ______________________ 14

15 Example 1 Compare the graph of each function with the graph of f (x) = x 3 without using your graphing calculator. a. g(x) = x 3 – 1 b. h(x) = (x – 1) 3 c. k(x) = (x + 2)

16 Example 2 Use the graph of f (x) = x 2 to find an equation for g(x) and h(x). 16

17 Exploration 3 Compare the graph of each function with the graph of f (x) = x 2 by using your graphing calculator to graph the function and f in the same viewing window. Describe the transformation. a. g(x) = –x 2 b. h(x) = (–x) 2 17

18 Reflections in the Coordinate Axes Reflections in the coordinate axes of the graph of y = f (x) are represented as follows: 1. h(x) = –f (x) _______________________ 2. h(x) = f (–x) _______________________ 18

19 Example 3 Use the graph of f (x) = x 4 to find an equation for g(x) and h(x). 19

20 Example 4 Compare the graph of each function with the graph of 20

21 Exploration 4 Graph the following functions in the same viewing window: y = cx 3, where c = 1, 4 and ¼. Describe the effect that c has on the graph. 21

22 Exploration 5 Graphing the following functions in the same viewing window: y = (cx) 3, where c = 1, 4 and ¼. Describe the effect that c has on the graph. 22

23 Nonrigid Transformations Rigid Transformation Changes position of the graph but maintains the shape of the original function.  Horizontal or vertical shifts and reflections. Nonrigid Transformation Causes a distortion in the graph. Changes the shape of the original graph.  Vertical or horizontal stretches and shrinks. 23

24 Vertical Stretch or Shrink Original function y = f (x). Transformation y = c f (x). Each y -value is multiplied by c.  Vertical stretch if c > 1.  Vertical shrink if 0 < c < 1. 24

25 Horizontal Stretch or Shrink Original function y = f (x). Transformation y = f (cx). Each x -value is multiplied by 1/c.  Horizontal shrink if c > 1.  Horizontal stretch if 0 < c < 1. 25

26 Homework 1.4 Worksheet 1.4  #5, 7, 11, 13, 16, 20, 24, 26, 27, 33, 37, 39, 42, 45, 47, 51, 53, 57, 61, 63, 67 26

27 27


Download ppt "Chapter 1 Functions and Their Graphs. Warm Up 1.4 A Norman window has the shape of a square with a semicircle mounted on it. Find the width of the window."

Similar presentations


Ads by Google