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# Functions and Their Graphs Practice Problems

based on 2 ratings
By McGraw-Hill Professional
Updated on Oct 4, 2011

To review these concepts, go to Functions and Their Graphs Help

## Functions and Their Graphs Practice Problems

#### Problems

1. Is the graph in Figure 3.9 the graph of a function?

Fig. 3.9.

2. Refer to the graph of f ( x ) in Figure 3.10.

Fig. 3.10.

(a) What is f (−3)?

(b) What is f (5)?

(c) What is the domain?

(d) What is the range?

(e) What are the x -intercepts?

(f) What is the y -intercept?

(g) What is/are the increasing interval(s)?

(h) What is/are the decreasing interval(s)?

3. Refer to the graph of f ( x ) in Figure 3.11.

Fig. 3.11 .

(a) What is f (2)? f (1)?

(b) What are the x -intercepts? What is the y -intercept?

(c) What is the domain? Range?

(d) What is the increasing interval? What are the decreasing intervals?

#### Solutions

1. No. The graph fails the Vertical Line Test.

2. (a) f (−3) = 1 because (−3, 1) is a point on the graph.

(b) f (5) = −5 because (5, −5) is a point on the graph.

(c) The domain is [−5, 5].

(d) The range is [−5,4].

(e) The x -intercepts are−4, − 1, and 3.

(f) The y -intercept is .

(g) The increasing intervals are (−4, −3) and (2, 3).

(h) The decreasing intervals are (−5, −4), (−3, 2) and (3, 5).

3. (a) f (2) = 4 because (2,4) is a point on the graph. f (1) = 2 because (1, 2) is a point on the graph.

(b) The x -intercepts are 0 and 3. The y -intercept is 0.

(c) The domain and range are each all real numbers, (−∞, ∞).

(d) The increasing interval is (0, 2), and the decreasing intervals are (−∞, 0) and (2, ∞).

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