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Chapter 11: Q. 387 (page 1069)

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

fx=x+2

Short Answer

Expert verified

a) The domain of the function is[0,鈭�)

b) Graph of the function is

c) Range of the function is[2,鈭�)

Step by step solution

01

Step 1. Given information.

The following expression is given:

fx=x+2

02

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

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

x鈮�0

In interval notation, the domain of the function will be

[0,鈭�)

03

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

To construct the graph of the function, we select some sample points in the interval [0,鈭�). Then we create a sample chart:

Using the sample chart, the graph of the function is constructed.

04

Step 4. Finding (c) The range of the function from the y values of the function are greater than or equal to 2. So, the range of the function will be[2,∞)

From the graph, we see that the range of the function will be[2,鈭�)

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