Math 3 - Transformations of Functions

Math 3 - Transformations of Functions

Open Ended

In the equation y=af(x-h)+k, what does the a do to the parent function?

Open Ended

In the equation y=af(x-h)+k, what does the h do to the parent function?

Open Ended

In the equation y=af(x-h)+k, what does the k do to the parent function?

Here are the rules, in case you needed a reminder :)

MAKE SURE you have this written down somewhere :)

Let's start with some parent function review

DONT forget about those :)

Multiple Choice

Which parent function matches the graph?

• y = |x|
• y = x
• y = x²
• y = 2^x

Multiple Choice

What type of function is shown?

• absolute value
• quadratic
• linear
• exponential

Multiple Choice

What type of function is shown?

• linear
• quadratic
• square root
• absolute value

Multiple Choice

Name the parent function.

• linear
• quadratic
• cube root
• cubic

Multiple Choice

What type of function is shown?

• cube root
• square root
• logarithm
• exponential

Multiple Choice

Which parent function is this?

• Quadratic

• Cubic

• Linear

• Rational

Now we will do transformations on a graph

Basically, what happened to get from the parent graph to the new graph?

Multiple Choice

Which equation represents this graph.

• f(x)=(x - 4)² - 3
• f(x)=-(x - 4)² + 3
• f(x)=(x - 4)² + 3
• f(x)=-(x + 4)² + 3

Multiple Choice

If the blue function is f(x)=x², then the red function must be

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Multiple Choice

  The blue function is the parent function f(x) = x³.  Which of the following is the correct equation for the red function, g(x)?

• g(x)=x³+1
• g(x)=x³-1
• g(x)=(x-1)³
• g(x)=(x+1)³

Multiple Choice

If the blue function is f(x)=√x, the red function must be

• g(x)=√(-x)
• g(x)=√(x-1)
• g(x)=√x-1
• g(x)=-√x

Multiple Choice

• Reflection over y-axis; Right 3; Up 1
• Right 3; Up 1
• Reflection over x-axis; Left 3; Up 1
• Reflection of x-axis; Right 3; Up 1

Multiple Choice

• Left 2; Up 2
• Right 2; Down 2
• Left 2; Up 2; Reflection over x-axis
• Vertical stretch by factor of 3; Right 2; Down 2

Multiple Choice

What is the equation of the graph?

• y = -√(x + 5)

• y = √(x) - 2

• y = √(x - 3)

• y = -√(x) + 3

Multiple Choice

Identify the transformations to this absolute value function: 

• x-axis reflection; up 4
• up 4
• x-axis reflection; down 4
• stretch of -2; up 4

Multiple Choice

Identify the transformations:

• Shrink of 2; up 5
• Stretch of 2; up 5
• Up 2; left 5
• Up 2; right 5

Multiple Choice

Identify the transformations:

• x-axis reflection; right 3
• x-axis reflection; left 3
• shrink of -1; right 3; up 3
• stretch of -1; right 3

And last but not least...

Transformations from an EQUATION (use the formula from the beginning!)

Multiple Choice

Which quadratic function is represented by the graph?

• y = 2(x - 4)² + 5
• y = 2(x + 4)² + 5
• y = -2(x - 4)² + 5
• y = -2(x + 4)² + 5

Multiple Choice

How did we transform from the parent function?
g(x) = -1/5(x - 1)² + 7

• reflection, vertical compression, horizontal right, vertical up
• vertical compression, horizontal shift left, vertical shift up
• reflection, horizontal shift right, vertical shift down
• no changes were made to y = x²

Multiple Choice

Describe the parent graph transformation

• stretch by 1/2, left 1, down 3
• stretch by 1/2, right 1, down 3
• compression by 1/2, left 1, down 3
• compression by 1/2, right 1, down 3

Multiple Choice

Describe the transformations from the original parent function f(x) = x².
g(x) = 5x² + 2

• Vertical Stretch of 5
  Down 2
• Vertical Shrink of 5
  Up 2
• Vertical Stretch of 5
  Up 2
• Vertical Shrink of 5
  Down 2

Multiple Choice

Tell how the function transformed from y =|x|
y = -2|x|

• Translated left 2 units
• Reflected over x-axis
• Stretched vertically and reflected over x-axis
• Compressed vertically and reflected over the x-axis

Multiple Choice

Which equation is a quadratic function reflected over the x-axis and shifted up 2.

• y = x² + 2
• y = -x² + 2
• y = x² - 2
• y = -(x + 2)²

Multiple Choice

Describe the transformations that maps
y = g(x) to y = - g(x + 6) - 10

• Reflect over y-axis
  Shifted down 10 units
  Shifted left 6 units
• Reflect over x-axis
  Shifted up 10 units
  Shifted left 6 units
• Reflect over y-axis
  Shifted up 10 units
  Shifted right 6 units
• Reflect over x-axis
  Shifted down 10 units
  Shifted left 6 units

Multiple Choice

Which equation describes the transformation of shifting f(x)=x² two units right?

• x² + 2
• x² - 2
• (x + 2)²
• (x - 2)²

Multiple Choice

What are the transformations of this functions compared to the parent function y = √(x)?

• Shifted right 5, shifted down 2, and reflected over the x-axis
• Reflected over the x-axis, vertical stretch, and shifted right 5
• Reflected over the x-axis, vertical stretch, and shifted left 5
• Shifted right 5, shifted down 2

Multiple Choice

Given f(x) = (x-3)² + 5.  What transformations took place from the original function f(x)?

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

Poll

On a scale of 1-5 (5 being the highest), how comfortable do you feel with this content?

• 1

• 2

• 3

• 4

• 5