Transformations of Functions Practice

• Stretch of 1/3

  Up 2

• Shrink of 1/3

  Up 2

• Stretch of 1/3

  Down 2

• Shrink of 1/3

  Down 2

Answer explanation

Hint: The parent function is x²

So the 1/3 is being multiplied to x, which is going to be either a shrink or stretch.

The + 2 is NOT inside parenthesis with x so it is going to go up or down.

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If the blue is f(x)=x^2, the red must be

• g(x)=(x+3)²
• g(x)=(x-3)²
• g(x)=x²+3
• g(x)=x²-2

Answer explanation

The red graph is 3 units to the right of the blue one right?

So pay attention to which rule will move the graph to the right. Hint: needs to be inside parenthesis

Which equation describes the transformation of shifting f(x)=x² seven units up?

• x³+7
• x³-7
• (x-7)³
• (x+7)³

Answer explanation

If we have a + 7 that is NOT inside parenthesis with x, then that means it is either going up or down.

The PLUS 7 means we are going up.

Given f(x) = (x-3)² + 5.

What transformations took place from the parent function?

• Left 3 and up 5
• Right 3 and down 5
• Left 3 and down 5
• Right 3 and up 5

Answer explanation

If the number is INSIDE the parenthesis then it affects the graph going LEFT or RIGHT.

If the number is OUTSIDE the parenthesis then it affects going UP or DOWN.

Match the equation to its description.

• Right 2 and up 2
• Left 2 and up 2
• Right 2 and down 2
• Left 2 and down 2

Answer explanation

If the number is INSIDE the parenthesis then it affects the graph going LEFT or RIGHT.

If the number is OUTSIDE the parenthesis then it affects going UP or DOWN.

Which transformation will occur if f(x) = x² is replaced with f(x) = 2x²?

• Vertical Compression by a factor of 2
• Vertical Stretch by a factor of 2
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Answer explanation

If we are multiplying by a number BIGGER than 1, than it is a STRETCH

• Vertical Compression by a factor of 1/2
• Vertical Stretch by a factor of 1/2
• Vertical translation up by 2 units.
• Reflection across the x-axis.

Answer explanation

If we are multiplying by a number LESS THAN 1, then it is a shrink/compression

In the equation f(x)=5(x+3)²-10 what effect does the 5 do when compared to the parent function?

• Vertical stretch by a factor of 5

• Vertical compress by a factor of 5

• Reflect over x-axis

• Vertical shift up 5 units

Answer explanation

Ignore the +3 and -10 since the question is JUST asking for the 5.

So if you need to, just graph what happens when you multiply the parent function by 5 and you will see what transformation happens.

Match the following parent functions with their graphs

• f(x) = x

• 
• f(x) = |x|

• 
• f(x) = x²

• 

Answer explanation

Use your notes for this one

There are two transformations happening to this function. Mark which two answer choices are correct.

• Reflect over x-axis

• Move 3 units left

• Move 3 units right

• Reflect over y-axis

Answer explanation

The negative is NOT inside with x and the + 3 is inside. So look at your rules or graph this in a calculator to see what will happen.