1.1 Horizontal and Vertical Translations

5 units right

D: [3 , 7]

R: [0 , 2]

(x+3 , y-2)(x , y)

(-7 ,4)

(-2,-1)

(0, -1)

(2, -3)

(7 , 2)

(-4 ,2)

(1 ,-3)

(3, -3)

(5, -5)

(10, 2)

Example 6Determine the equation of the translated function in the form y – k = f (x – h)

Horizontal and Vertical TranslationsThe following graphs are all translations of the function y = x2. Drag each function equation so that it labels the correct graph.

Chapter

1

a) b) c)

Click to reveal the correct answer.

y = (x ! 3)2 y = x2 + 3y + 2 = x2

y + 2 = x2 y = x2 + 3 y = (x ! 3)2

Horizontal and Vertical TranslationsThe graph of y = |x| is translated to y = |x + 3| + 5. Use thePen tool to answer the following questions.

Chapter

1

a) What is the image of the point (0, 0) under this translation?

b) Represent this translation as a mapping.

a) For y = |x + 3| + 5, h = !3 and k = 5. The point (0, 0) on the graph of y = |x| is transformed to become (!3, 5). The graph has been translated three units to the left and five units up.

b) (x, y) " (x + h, y + k) (x, y) " (x + (!3), y + 5) (x, y) " (x ! 3, y + 5)

Close the Screen Shade below to reveal the full solution.

Ans

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(a)

Ans

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(b)

(x, y) " ( x ! 3, y + 5)

Horizontal and Vertical TranslationsChapter

1 The graphs of the function y = x2 and a translation of this function are shown. Use the Pen tool to write the equation of the translated function.

The equation of the translated function is:

Close the Screen Shade below to reveal the full solution.

Locate the points on the graph of f(x) and the image pointson the graph of g(x).

f(x) g(x) (0, 0) " (!2, 4) (1, 1) " (!1, 5) (!1, 1) " (!3, 5) (2, 4) " (0, 8) (!2, 4) " (!4, 8) ( x, y) " (x ! 2, y + 4)Therefore, h = !2 and k = 4.

The equation of the translated function is y ! k = f(x ! h) y ! 4 = ( x ! (!2)) 2

y ! 4 = ( x + 2)2

or y = (x + 2)2 + 4

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Horizontal and Vertical TranslationsChapter

1 The graph of the function f(x) is shown in blue. Ariane was asked to graph g(x) = f(x + 3) – 2 . She drew the red graph. What mistake did Ariane make?

Ans

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Ariane translated the graph 3 units right and 2 units down. She should have translated it 3 units left and 2 units down.