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Function Transformation Worksheet - Grade 11

Describe shifts, reflections, and stretches using function notation. Includes a worked example, printable practice, and an answer key with explanations.

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Grade 11 Math Functions OperationsFunction Transformation

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Includes

2 TextMultiple ChoiceFill in the BlanksShort AnswerTrue / FalseCustom

Standards

CCSS.MATH.CONTENT.HSF.BF.B.3
9 sections · Free to use · Printable
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Function Transformation - Grade 11

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Learning goal and worked example

Describe shifts, reflections, and stretches using function notation.

For y = 3f(x−2)+1, shift right 2, multiply output by 3, then shift up 1. The negative sign inside x−2 corresponds to a shift right.

Prerequisite: evaluating functions. For horizontal scale, y = f(bx) uses scale factor 1/|b|.

Read each question carefully and provide your answers in the space provided. Show all your work for full credit.

1. If the graph of y = f(x) is shifted 3 units to the right, what is the new equation?

a

y = f(x) + 3

b

y = f(x) - 3

c

y = f(x + 3)

d

y = f(x - 3)

2. What transformation occurs when y = -f(x)?

a

Reflection across the x-axis

b

Reflection across the y-axis

c

Vertical shift down

d

Horizontal shift left

3. A vertical stretch by a factor of 2 applied to y = f(x) results in the equation y =  .

4. The graph of y = f(x) + k shifts the graph   by k units if k > 0.

5. Describe the transformations applied to y = x² to obtain the graph of y = -2(x + 1)² - 4.

6. The transformation y = f(0.5x) represents a horizontal compression.

T

True

F

False

7. Sketch the graph of y = -(x - 2)² + 3, given the parent function y = x².

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

Answer key and worked solutions

1. d: y=f(x−3). 2. a: reflection across the x-axis. 3. 2f(x). 4. Up.

5. Shift left 1, stretch vertically by 2, reflect across the x-axis, then shift down 4. Vertex (−1,−4); opens downward.

6. False: f(0.5x) is a horizontal stretch by factor 2.

7. Vertex (2,3), axis x=2, opens downward. Plot (1,2),(3,2),(0,−1),(4,−1). Domain ℝ; range (−∞,3]. The x-intercepts are 2±√3 and the y-intercept is −1.

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