Download presentation

Published bySonny Rockhill Modified over 5 years ago

1
**How do we perform transformations of functions?**

Standards: MM4A4. Students will investigate functions. a. Compare and contrast properties of functions within and across the following types: linear, quadratic, polynomial, power, rational, exponential, logarithmic, trigonometric, and piecewise. b. Investigate transformations of functions. c. Investigate characteristics of functions built through sum, difference, product, quotient, and composition.

2
**In your own words, describe what a parent function is.**

3
**What the graph will look like.**

Function Name y = x linear y = -x y = ×2 quadratic y = -×2 y = x3 Cubic y = -x3 y = lxl absolute value y = -lxl y = 2x exponential y = -(2x) rational y = 1/x square root

4
**Shifting Graphs: aka Translations**

Suppose c>0 y=f(x)+c→shifts f(x) c units up y=f(x)- c→shifts f(x) c units down y=f(x-c) →shifts f(x) c units right y=f(x+c)→shifts f(x) c units left

5
**Stretching Graphs: aka Dilations**

Suppose c>1 y=cf(x) →stretches f(x) vertically by a factor of c. This means the graph is narrower y = f(x)/c →compresses f(x) vertically by a
factor of c. This means the graph is wider y = f(cx) →compresses f(x) horizontally by a
factor of c. This means the graph is narrower y=f(x/c) →stretches f(x) horizontally by a
factor of c. This means the graph is wider

6
**Reflecting Graphs: aka Reflections**

y=-f(x) →reflects f(x) about
the x-axis y=f(-x) →reflects f(x)
about the y-axis

7
Sketch y = x2-1

8
Sketch y = x2-1

9
Sketch y = x2-1 Now Sketch y=|x2-1|

10
Sketch y = x2-1 Now Sketch y=|x2-1|

11
**Given f(x) the graph, Perform the
transformation to create f(x - 2) + 3.**

12
**Given f(x) the graph, Perform the
transformation to create -f(x).**

13
**Given f(x) the graph, Perform the
transformation to create f(-x).**

14
**Given f(x) the graph, Perform the
transformation to create f(x + 2) - 3.**

15
**Given f(x) the graph, Perform the
transformation to create -f(x - 5) .**

16
**Given f(x) the graph, Perform the
transformation to create -(f(x - 4) + 1).**

17
**Which of the following graphs is the graph of the function ?**

1 Which of the following graphs is the
graph of the function ? 1. A 2. B 3. C

18
Homework P. 48 # 1-8 Graph each function and describe the transformations.

Similar presentations

© 2020 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google