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4.5 – Stretching Functions Vertically
Objectives
 Determine the equation of a function G(x) whose graph has been vertically stretched or compressed from the graph of F(x) when you are given the equation of F(x).
 Describe how the graph of a function changes when the function is multiplied by a positive or negative number.
 Determine the equation of a function G(x) whose graph has been either vertically stretched and shifted or vertically compressed and shifted from the graph of F(x) when you are given the equation of F(x).
Key Terms
 Compress – To make something shorter (flatter & wider).
 Stretch – To make something longer (taller & more thin).
Review
 To move functions vertically, add or subtract the yvalue at the end of the equation
 To move functions horizontally, subtract a positive (right) or subtract a negative (left) xvalue from the xpart of the equation
 Left: (x – (#)), which becomes (x + #)
 Right: (x – (+#)), which becomes (x – #)
Notes
Vertically Stretching and Compressing 
 Vertically stretching and compressing a function changes the yvalue for each coordinate
 Vertically stretching or compressing functions changes the SHAPE of the graph
 Stretching: larger yvalues (positive or negative numbers larger than 1)
 Compressing: smaller yvalues (positive or negative numbers less than 1: decimals and fractions)
 Remember: parent functions have yvalues that equal 1
 1y can be written as just “y”
 # = 1
 Stretching Example (Blue to Red)
 The Red function, G(x), is stretched by 2 from the Blue function, F(x), below
 Notice that all yvalues are 2 times larger (doubled)
 Blue, F(x):
 Red, G(x):
 Simplied to:
 Stretching and Compressing Examples

Flipping Over Axes 
 Explanation of Stretching, Compressing, and Flipping Over the xaxis
 When you multiply a function by 1, what is the effect on its graph?
 Answer: the graph flips over the xaxis
 Examples of Stretched and Compressed Functions Flipped Over the xaxis
 – 0.8 is compressed from the parent function because its value is between zero and 1.
 The negative means the function is flipped over the xaxis.
 – 3 is stretched from the parent function because its value is greater than 1.
 The negative means the function is flipped over the xaxis.
 Flipping Over the yaxis
 Not every part of the function is affected (such as the case with flipping over the xaxis).
 ONLY the xvalues are affected, just like when you shift to the left or to the right
 Notice that the x (inside the parenthesis) has changed signs
 Example: Flipping Over the yaxis
 Blue, F(x):
 Red, G(x):
 Simplify:

More Examples 
 Quiz Example 1
 Parent:
 Shift 7 units Up
 Shift 2 units to the Left
 Stretch vertically by 3
 Answer:
 Quiz Example 2
 Parent:
 Shift 1 unit Down
 Shift 4 units to the Right
 Compress Vertically by 0.2
 Answer:
 Quiz Example 3
 Parent:
 Shift 9 Units Up
 Shift 3 Units to the Right
 Stretch Vertically by 8 (it flipped over the xaxis)
 Answer:
 Quiz Example 4
 Parent:
 Shift 2 Units Down
 Shift 4 Units to the Right
 Compress Vertically by 0.6 (it flipped over the xaxis)
 Answer:
 Quiz Example 5
 Parent:
 Shift 3 Units Up
 Shift 6 Units to the Right
 Compress Vertically by 0.2 (flipped over xaxis)
 Flip Over the yaxis
 Answer:

Important!
Practice (Apex 4.5)
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