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Found in: Page 351

### Precalculus Mathematics for Calculus

Book edition 7th Edition
Author(s) James Stewart, Lothar Redlin, Saleem Watson
Pages 948 pages
ISBN 9781337067508

# Match the logarithmic function with its graph.$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)={\mathrm{log}}_{2}x\left(\mathrm{b}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)={\mathrm{log}}_{2}\left(-x\right)\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)=-{\mathrm{log}}_{2}x\left(\mathrm{d}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)=-{\mathrm{log}}_{2}\left(-x\right)\end{array}$

1. The graph of (a) is III.
2. The graph of (b) is II.
3. The graph of (c) is I.
4. The graph of (d) is IV.
See the step by step solution

## Part a. Step 1. Given.

The given expression is $f\left(x\right)={\mathrm{log}}_{2}x$.

## Part a. Step 2. To determine.

We have to find a graph for the given function.

## Part a. Step 3. Calculation.

We make a table for $f\left(x\right)={\mathrm{log}}_{2}x$:

 x 1 2 4 $f\left(x\right)$ 0 1 2

So, the graph is:

This graph matches with graph III.

So, the graph of (a) is III.

## Part b. Step 1. Given.

The given expression is $f\left(x\right)={\mathrm{log}}_{2}\left(-x\right)$.

## Part b. Step 2. To determine.

We have to find a graph for the given function.

## Part b. Step 3. Calculation.

We make a table for $f\left(x\right)={\mathrm{log}}_{2}\left(-x\right)$:

 x $-1$ $-2$ $-4$ $f\left(x\right)$ 0 1 2

So, the graph is:

This graph matches with graph II.

So, the graph of (b) is II.

## Part c. Step 1. Given.

The given expression is $f\left(x\right)=-{\mathrm{log}}_{2}x$.

## Part c. Step 2. To determine.

We have to find a graph for the given function.

## Part c. Step 3. Calculation.

We make a table for $f\left(x\right)=-{\mathrm{log}}_{2}x$:

 x 1 2 4 $f\left(x\right)$ 0 $-1$ $-2$

So, the graph is:

This graph matches with graph I.

So, the graph of (c) is I.

## Part d. Step 1. Given.

The given expression is $f\left(x\right)=-{\mathrm{log}}_{2}\left(-x\right)$.

## Part d. Step 2. To determine.

We have to find a graph for the given function.

## Part d. Step 3. Calculation.

We make a table for :

 x $-1$ $-2$ $-4$ $f\left(x\right)$ 0 $-1$ $-2$

So, the graph is:

This graph matches with graph IV.

So, the graph of (d) is IV.