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# Translations and Special Functions Help (page 3)

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By McGraw-Hill Professional
Updated on Oct 4, 2011

## Translations and Special Functions Practice Problems

#### Practice

Directions: For 1-4, match the graph with its function. Some functions will be left over.

1.

Fig. 5.25

2.

Fig. 5.26

3.

Fig. 5.27

4.

Fig. 5.28

Directions: For Problems 5-8, use the statements below to describe the transformations on f (x). Some of the statements will be used more than once, and others will not be used.

(A) shifts the graph to the left.

(B) shifts the graph to the right.

(C) shifts the graph up.

(D) shifts the graph down.

(E) reflects the graph across the y -axis.

(F) reflects the graph across the x -axis.

(G) vertically compresses the graph.

(H) vertically stretches the graph.

(I) reflects the graph across the x -axis and vertically compresses the graph.

(J) reflects the graph across the y -axis and vertically stretches the graph.

1. For the function f (− x ) + 3,

(a) What does “+3” do?

(b) What does the negative sign on x do?

For the function 3 f ( x − 1) − 4,
2. (a) What does “3” do?

(b) What does “−1” do?

(c) What does “−4” do?

3. For the function ,

(a) What does ,

(b) What does

(c) What does

4. For the function ,

(a) What does

(b) What does the negative sign on x do?

(c) What does “−1” do?

Refer to the graph of f ( x ) in Figure 5.29 for Problems 9-10.

Fig. 5.29

1. Sketch the graph of f (− x ) −1.

2. Sketch the graph of .

#### Solutions

1. C, E
2. H, B, D
3. I, A, C
4. G, E, D
5. Fig. 5.30

Table 5.5

 Original point Opposite of x − x Down 1 y − 1 Plot this (−5,−3) −(−5) = 5 −3 − 1 = −4 (5,−4) (−2, 0) −(−2) = 2 0 − 1 = −1 (2,−1) (0, 4) −0 = 0 4 − 1 = 3 (0, 3) (5,−2) −5 −2 − 1 = −3 (−5,−3)
6.

Fig. 5.31

Table 5.6

 Original point Left 3 x − 3 Opposite of y , compressed, up 1         − y + 1 Plot this point (−5, −3) −5 − 3 = −8 − (−3) + 1 = (−8, ) (−2, 0) −2 − 2 = −5 − (0) + 1 = 1 (−5, 1) (0,4) 0 − 3 = −3 − (4) + 1 = −1 (−3,−1) (5, −2) 5 − 3 = 2 − (−2) + 1 = 2 (2, 2)

Find practice problems and solutions for these concepts at Translations and Special Functions Practice Test.

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