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Graph each function. State the domain and range.

f(x)={x2ifx<13xifx1}

Short Answer

Expert verified

The domain is all real numbers and the range is

{y:y3ory<1}

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=f(x)=x2;x<13x;x1

02

Step 2. Make a table for the given function.

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

x

x1

x<1

y=f(x)=x2;x<13x;x1

-1

No

Yes

-3

0

No

Yes

-2

1

Yes

No

3

2

Yes

No

6

3

Yes

No

9

03

Step 3. Plot the graph.

Plot the values ofx and 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-coordiante values specify the range of the function. Since, the graph does not take any value less thany=3 and more than or equal to y=1, the range is{y:y3ory<1}.

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