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Q4.

Expert-verifiedFound in: Page 351

Book edition
7th Edition

Author(s)
James Stewart, Lothar Redlin, Saleem Watson

Pages
948 pages

ISBN
9781337067508

**Match the logarithmic function with its graph.**

$\begin{array}{l}\left(\mathrm{a}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)={\mathrm{log}}_{2}x\left(\mathrm{b}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)={\mathrm{log}}_{2}\left(-x\right)\\ \left(\mathrm{c}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)=-{\mathrm{log}}_{2}x\left(\mathrm{d}\right)\text{\hspace{0.17em}\hspace{0.17em}}f\left(x\right)=-{\mathrm{log}}_{2}\left(-x\right)\end{array}$

- The graph of (a) is III.
- The graph of (b) is II.
- The graph of (c) is I.
- The graph of (d) is IV.

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

We have to find a graph for the given function.

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.

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

We have to find a graph for the given function.

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.

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

We have to find a graph for the given function.

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.

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

We have to find a graph for the given function.

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.

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