Shifting a Function’s Graph
Lesson 5.1
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
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
Use different styles for
each of the functions
• Before you graph the other two lines, predict
what you think will be the result.
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
Which Way Will You Shift?
Matching -- match the letter of the list on the right
with the function on the left.
1.
2.
3.
4.
5.
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
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
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?
Make It Shift
• To move the graph down 4 units and left 7
units use the transformation
f(x + 7) - 4
Numerical Results
• Given the function
defined by a table
x
-3
-2
-1
0
1
2
3
f(x)
7
4
9
3
12
5
6
• Determine the value of the following
transformations
f(x) + 3
f(x + 1)
f(x - 2)
Assignment
• Lesson 5.1
• Page 200
• Exercises 1 – 41 odd