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.