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Graph each function. State the domain and range.

fx=2x3ifx2x+1ifx>2

Short Answer

Expert verified

The domain is all real numbers and the range is {y:y>3ory1}.

Step by step solution

01

Step 1. State the concept for the given function.

This is a piece-wise defined function. Check for different values in the domain and include the values for which the function changes :

y=fx=2x3;x2x+1;x>2

02

Step 2. Make a table for the given function.

Construct a table for f(x)by taking some values of x.

x

x>2

x2
y=fx=2x3;x2x+1;x>2

0

No

Yes

-3

1

No

Yes

-1

2

No

Yes

1

3

Yes

No

4

4

Yes

No

5

03

Step 3. Plot the graph.

Plot the values of xand f(x)on a graph,

The x-coordinate values specify the domain of the function. Since the graph covers all possible values of x, the domain is all real numbers.

The y-coordinate values specify the range of the function. Since, the graph does not take any value less than or equal toy=3and more than y=1, the range is y:y>3ory1.

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