Describe the transformation of y = f(x) for the new function y = f(x) - 5

The graph of y = f(x) was shifted down 5 units.

The graph of y = f(x) was shifted to the right 5 units.

The graph of y = f(x) was shifted to the left 5 units.

The graph of y = f(x) was shifted up 5 units.

Stretched 6 and reflected over the y-axis

Stretched 6 and reflected over the x-axis

Shrunk 6 and reflected over the y-axis

Shrunk 6 and reflected over the x-axis

Let f(x)=√(x) and g(x)= -3√(x-2)+1. Describe g(x) in terms of f(x):

flip over x axis, vertical stretch, right 2, up 1

flip over y axis, vertical compression, left 2, up 1

flip over x axis, vertical stretch, left 2, up 1

flip over y axis, vertical compression, right 2, up 1

Describe the transformation of the equation below from the parent function of y = I x I y = -2 I x - 3 I + 3

reflected over x axis, stretched by 2, right 3, up 3

reflected over x axis, stretched by 2, left 3 up 3.

reflected over x axis, shrunk by 2, right 3, up 3

reflected over the x axis, shrunk by 2, left 3, up 3

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

Vertical Stretch by a factor of 2

Vertical Compression by a factor of 2

Vertical translation up by 2 units.

Which transformation will occur if f(x) = x 2 is replaced with 1/2⋅f(x)?

Vertical Compression by a factor of 1/2

Vertical Stretch by a factor of 1/2

Vertical translation up by 2 units.

Describe the transformation of y = g(x) for the function y = 3g(x - 3) + 5

Shifted up 5 units Shifted right 3 units Stretched vertically by a factor of 3

Shifted up 5 units Shifted left 3 units Stretched vertically by a factor of 3

Shifted down 5 units Shifted left 3 units Stretched vertically by a factor of 3

Shifted down 5 units Shifted left 3 units Stretched vertically by a factor of 1/3

What causes the graph of y = x 2 to open downward?

multiply the x 2 by a negative number

multiply the x 2 by a number greater than 1

Reflect over x-axis Shifts down 2

Reflect over y-axis Shifts up 2

Reflect over x-axis Shifts up 2

Reflect over y-axis Shifts down 2

Does the table represent a function?

No, there is a repeated x-value.

Yes, there is a repeated x-value.

No, there aren't any repeated y-values.

Yes, there are repeated y-values.

Function transformations

Authored by Michelle Owen

Mathematics

10th - 11th Grade

CCSS covered

Used 69+ times

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53 questions

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MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

f(x - 3)

f(x + 3)

f(x) + 3

f(x) - 3

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

f(x + 2)

f(x) + 2

f(x - 2)

f(x) - 2

Tags

CCSS.HSF.BF.B.3

CCSS.HSF.IF.C.7

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The original graph is f(x). The new graph has been reflected across the x axis. The equation for the new graph in f(x) notation is:

-f(x)

f(-x)

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

CCSS.HSG.CO.A.4

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The original graph is f(x). The new graph is vertically stretched by a factor of 2. What is the equation for the new graph?

2f(x)

f(2x)

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

f(x + 3) - 4

f(x - 4) + 3

f(x + 4) + 3

f(x + 3) + 4

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The original graph is f(x). The new graph has been reflected across the y-axis and moved 6 to the right. Which of the following represents the new graph?

f(x - 6)

-f(x + 6)

f(-x - 6)

f(-x + 6)

Tags

CCSS.HSF.BF.B.3

MULTIPLE CHOICE QUESTION

2 mins • 1 pt

The original graph is f(x). The new graph is up 5, left 3, and reflected across the x-axis.

f(x + 3) + 5

-f(x - 3) + 5

-f(x + 3) + 5

-f(x + 5) + 3

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

CCSS.HSG.CO.A.4

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Function transformations

If the original graph is f(x) and the new graph has been moved 3 to the right, how would one write that in function notation?

If the original graph is f(x), and the new graph has been moved two to the left, what would be the new graph in f(x) notation?

The original graph is f(x). The new graph has been reflected across the x axis. The equation for the new graph in f(x) notation is:

The original graph is f(x). The new graph is vertically stretched by a factor of 2. What is the equation for the new graph?

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

The original graph is f(x). The new graph has been reflected across the y-axis and moved 6 to the right. Which of the following represents the new graph?

The original graph is f(x). The new graph is up 5, left 3, and reflected across the x-axis.

The original graph is f(x). The new graph has been vertically stretched by a factor of 4 and translated down 4.

Name the parent function.

Name the parent function.

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