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Q56.

Expert-verifiedFound in: Page 274

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 $\left\{y:y>3\text{or}y\le 1\right\}$.

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

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

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 |

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 $\left\{y:y>3\text{or}y\le -1\right\}$.

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