1. Shifting a Function’s Graph
Lesson 5.1

2. Tools for Exploration Consider the function f(x) = 0.1(x3 – 9x2)
Enter this function into your calculator on the y= screen
Set the window to be  -10 < x < 10   and   -20 < y < 20
Graph the function

3. Use different styles for each of the functions
Shifting the Graph
Enter the following function calls of our original function on the y= screen:
y1=  0.1 (x3 - 9x2) 
y2=   y1(x + 2) 
y3=   y1(x) + 2
Before you graph the other two lines, predict what you think will be the result.
Use different styles for each of the functions

4. Shifting the Graph How close were your predictions?
Try these functions – again, predict results
y1=  0.1 (x3 - 9x2) 
y2=   y1(x - 2) 
y3=   y1(x) - 2

5. Which Way Will You Shift?
Matching -- match the letter of the list on the right with the function on the left.
f(x) + a
f(x - a)
f(x)*a
f(x + a)
f(x) - a
A) shift down a units  B) shift right a units  C) shift left a units  D) shift up a units  E) turn upside down  F) none of these

6. Which Way Will It Shift? 
It is possible to combine more than one of the transformations in one function:
What is the result of graphing this transformation of our function, f(x)?
f(x - 3) + 5

7. Make It Shift It has been moved to the right 3 and up 5
Now what would you do if you wanted to move the graph down 4 units and left 7 units?

8. Make It Shift
To move the graph down 4 units and left 7 units use the transformation
f(x + 7) - 4

9. Numerical Results Given the function defined by a table
Determine the value of the following transformations x -3 -2 -1 1 2 3
f(x) 7 4 9 12 5 6
f(x) + 3
f(x + 1)   
f(x - 2)
   

10. Assignment
Lesson 5.1
Page 200
Exercises 1 – 41 odd