Functions and Their Graphs Practice Problems

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, ∞).