Stretches and Compressions of Linear Functions

Describe the transformation of the graph.

f(x) = 3x - 3

g(x) = x - 3

f(x)----> g(x)

• A vertical stretch. The slope and y-intercept are scaled by a factor of 1/3.

• A vertical compression. The slope and y-intercept are scaled by a fact of 1/3.

• A horizontal stretch. The slope is scaled by a factor of 1/3, the y-intercept is unchanged.

• A horizontal compression. The slope is scaled by a factor of 1/3, the y-intercept is unchanged.

Answer explanation

When we multiply the output by a constant k we are scaling the slope and the y-intercept by that constant.

f(x) ----> k f(x)

for k > 1 we get a vertical stretch

for 0 < |k| < 1 we get a vertical compression

When we multiply the input by a constant k we are scaling the slope by a factor of k, while the y-intercept remains unchanged.

f(x) ---> f(kx)

for k > 1 we get a horizontal compression.

for 0 < |k| < 1 we get a horizontal stretch

Describe the transformation of the graph.
f(x) = 3x - 3
g(x) = x - 1
f(x)----> g(x)

• A vertical stretch. The slope and y-intercept are scaled by a factor of 1/3.

• A vertical compression. The slope and y-intercept are scaled by a fact of 1/3.

• A horizontal stretch. The slope is scaled by a factor of 1/3, the y-intercept is unchanged.

• A horizontal compression. The slope is scaled by a factor of 1/3, the y-intercept is unchanged.

Answer explanation

When we multiply the output by a constant k we are scaling the slope and the y-intercept by that constant.

f(x) ----> k f(x)

for k > 1 we get a vertical stretch

for 0 < |k| < 1 we get a vertical compression

When we multiply the input by a constant k we are scaling the slope by a factor of k, while the y-intercept remains unchanged.

f(x) ---> f(kx)

for k > 1 we get a horizontal compression.

for 0 < |k| < 1 we get a horizontal stretch

What is this a picture of?

• A vertical stretch

• A vertical compression

• A horizontal stretch

• A horizontal compression

Answer explanation

You can tell the difference between a vertical/ horizontal stretch or compression because when a function is stretched or compressed vertically, both the slope and the y-intercept changes. You can tell it is horizontal when only the slope changes.

Unless it goes through the origin and had the y-intercept as 0 to start with!

What is the value of k for this vertical stretch?

• 2

• 1/2

• 5

• 1/5

The parent is in purple and transformed is in black. Which equation would result in the black?

• f(x) = |2x|

• f(x)=|x|+2

• f(x)=|x|+1/2

• f(x)=|1/2x|

Does the 3 represent a horizontal or vertical stretch/compression?

• Horizontal

• Vertical

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression

• Vertical Stretch

• Vertical Compression

• Horizontal Stretch

• Horizontal Compression