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Q. 34

Expert-verified
Found in: Page 284

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# The graph of an exponential function is given. Match each graph to one of the following functions.

(A) $y={3}^{x}$

See the step by step solution

## Step 1. Given

The graph whose equation need to found out is as:

## Step 2. Concept

Since for each of the graph asymptote is given we will find the equation of asymptote and will match with the options available.

## Step 3. Calculation

Considering the equations one by one we get:

$\left(A\right)\phantom{\rule{0ex}{0ex}}y={3}^{x}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }{3}^{x}\phantom{\rule{0ex}{0ex}}=\infty or0\phantom{\rule{0ex}{0ex}}whichisequaltoy=0$

$\left(B\right)\phantom{\rule{0ex}{0ex}}y={3}^{-x}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }{3}^{-x}\phantom{\rule{0ex}{0ex}}=0or\infty \phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$

$\left(C\right)\phantom{\rule{0ex}{0ex}}y=-{3}^{x}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }-{3}^{x}\phantom{\rule{0ex}{0ex}}=\infty or0\phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$

localid="1646201596483" $\left(D\right)\phantom{\rule{0ex}{0ex}}y=-{3}^{-x}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }-{3}^{-x}\phantom{\rule{0ex}{0ex}}=-\infty or0\phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$

$\left(E\right)\phantom{\rule{0ex}{0ex}}y={3}^{x}-1\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }{3}^{x}-1\phantom{\rule{0ex}{0ex}}=\infty or-1\phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$

$\left(F\right)\phantom{\rule{0ex}{0ex}}y={3}^{x-1}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }{3}^{x-1}\phantom{\rule{0ex}{0ex}}=\infty or0\phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$

$\left(G\right)\phantom{\rule{0ex}{0ex}}y={3}^{1-x}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }{3}^{1-x}\phantom{\rule{0ex}{0ex}}=\infty or0\phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$

$\left(H\right)\phantom{\rule{0ex}{0ex}}y=1-{3}^{x}\phantom{\rule{0ex}{0ex}}li{m}_{x\to ±\infty }y=li{m}_{x\to ±\infty }1-{3}^{x}\phantom{\rule{0ex}{0ex}}=-\infty or1\phantom{\rule{0ex}{0ex}}whichisnotequaltoy=0$