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Chapter 8: Q. 386 (page 833)

In the following exercise, (a) find the domain of the function (b) graph the function (c) use the graph to determine the range:

gx=x-4

Short Answer

Expert verified

(a)[4,鈭�)

(b)

(c)[0,鈭�)

Step by step solution

01

Step 1. Given information.

The following expression is given:

gx=x-4

02

Step 2. Finding (a) The domain of the function.

Since the radical has index 2, the radicand must be greater than or equal to zero.

If x-4鈮�0, then x鈮�4.

This tells us that the domain is all values x鈮�4.

In interval notation, this can be expressed as[4,鈭�)

03

Step 3. Drawing (b) Graph of the function.

To graph the function, we choose points in the interval [4,鈭�). We create a chart by taking some sample points and use that chart to plot the graph.

The graph of the function is shown below:

04

Step 4. Finding (c) Range of the function.

From the graph, we see that the y values are greater than or equal to 0. So, the range of the function will be[0,鈭�).

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