Math 3 - Transformations of Functions

Presentation

•

Mathematics

•

10th - 12th Grade

•

Medium

•

CCSS

HSF.BF.B.3, HSG.CO.A.2, HSF.IF.C.7

+11

Standards-aligned

Belle Turner

Used 3+ times

FREE Resource

5 Slides • 30 Questions

Math 3 - Transformations of Functions

Open Ended

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

Type response here

Open Ended

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

Type response here

Open Ended

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

Type response here

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?

Math 3 - Transformations of Functions

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