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Transformations: Vertical and Horizontal Stretch and Shrink

Explore vertical and horizontal stretches and shrinks of functions with this comprehensive worksheet for Grade 11 math students.

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Grade 11 Math GeometryTransformationsVertical and Horizontal Stretch and Shrink
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Includes

Fill in the BlanksMultiple ChoiceShort AnswerCustomTrue / False

Standards

CCSS.MATH.CONTENT.HSF.BF.B.3

Topics

mathgrade 11transformationsstretchshrinkfunctions
7 sections · Free to use · Printable
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Transformations: Vertical and Horizontal Stretch and Shrink

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Date:

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Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. A vertical stretch or shrink occurs when a function f(x) is multiplied by a constant 'a' such that the new function is g(x) = a * f(x). If |a| > 1, the graph undergoes a vertical  . If 0 < |a| < 1, the graph undergoes a vertical  .

2. A horizontal stretch or shrink occurs when the input 'x' of a function f(x) is multiplied by a constant 'b' such that the new function is g(x) = f(b * x). If |b| > 1, the graph undergoes a horizontal  . If 0 < |b| < 1, the graph undergoes a horizontal  .

3. If the graph of y = f(x) is vertically stretched by a factor of 3, the new equation is:

a

y = f(3x)

b

y = 3f(x)

c

y = f(x/3)

d

y = f(x) + 3

4. The graph of y = sin(x) is horizontally shrunk by a factor of 1/2. The new equation is:

a

y = 2sin(x)

b

y = sin(x/2)

c

y = sin(2x)

d

y = sin(x) - 2

5. Describe the transformation from the graph of f(x) to the graph of g(x) = 4f(x).

6. Describe the transformation from the graph of f(x) to the graph of h(x) = f(x/3).

7. The graph of y = x² is shown below. On the same grid, sketch the graph of y = (1/2)x².

-5-4-3-2-112345-5-4-3-2-112345

8. The graph of y = √x is shown below. On the same grid, sketch the graph of y = √(2x).

01234512345

9. A vertical stretch by a factor of 0.5 is the same as a vertical shrink by a factor of 2.

T

True

F

False

10. A horizontal shrink by a factor of 3 means replacing 'x' with '3x' in the function.

T

True

F

False

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