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Chapter 3: Q 527 (page 362)

In the following exercises, graph each function state its domain and range. Write the domain and range in interval notation.

f(x)=x2+2

Short Answer

Expert verified

The domain of the function is -鈭�.鈭�and range is [2,鈭�).

The graph of the function is shown below:

Step by step solution

01

Step 1. Given information

f(x)=x2+2

We need to graph the given function and state its domain and range in interval notation.

02

Step 2. Draw the table with different x values.

Put the different values ofxinto the given function and make the table as shown:

03

Step 3. Draw the graph by using the obtained table. 

The required graph is shown below:

04

Step 4. Determine the domain and range.

The domain of a function is the set of values for which the function is defined, and range is the set of all values which a function can produce.

From the graph, it can be observed that the function is defined for all real numbers and produce f(x)鈮�2.

Thus, the domain of the function is (-鈭�,+鈭�)and range is [2,鈭�).

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