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Expert-verified Found in: Page 274 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # Graph each function. State the domain and range. $f\left(x\right)=\left\{\begin{array}{l}2x-3\text{if}x\le 2\\ x+1\text{if}x>2\end{array}\right\}$

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

See the step by step solution

## 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 :

$y=f\left(x\right)=\left\{\begin{array}{c}2x-3;\text{}x\le 2\\ x+1;\text{}x>2\end{array}\right\}$

## Step 2. Make a table for the given function.

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

 $x$ $x>2$ $x\le 2$ $y=f\left(x\right)=\left\{\begin{array}{c}2x-3;\text{}x\le 2\\ x+1;\text{}x>2\end{array}\right\}$ 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 $f\left(x\right)$ 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 $\left\{y:y>3\text{or}y\le -1\right\}$. ### Want to see more solutions like these? 