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Q56.

Expert-verified

Algebra 1

Found in: Page 274

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

Graph each function. State the domain and range.
$f (x) = \{\begin{array}{l} 2 x - 3 if x \leq 2 \\ x + 1 if x > 2 \end{array}\}$

The domain is all real numbers and the range is ${y : y > 3 or y \leq 1}$ .

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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 :

$y = f (x) = \{\begin{matrix} 2 x - 3; x \leq 2 \\ x + 1; x > 2 \end{matrix}\}$

Step 2. Make a table for the given function.

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

$x$	$x > 2$	$x \leq 2$	$y = f (x) = \{\begin{matrix} 2 x - 3; x \leq 2 \\ x + 1; x > 2 \end{matrix}\}$
0	No	Yes	$- 3$
1	No	Yes	$- 1$
2	No	Yes	1
3	Yes	No	4
4	Yes	No	5

Step 3. Plot the graph.

Plot the values of $x$ 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 $y$ -coordinate values specify the range of the function. Since, the graph does not take any value less than or equal to $y = 3$ and more than $y = - 1$ , the range is $\{y : y > 3 or y \leq - 1\}$ .

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