Q. 33 - Precalculus Enhanced with Graphing Utilities

Question

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

Step-by-Step Solution

Answer

(B) $y=3^{-x}$

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:

$$\begin{gathered} \left(A\right) \\ y=3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^x \\ =\infty or 0 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(B\right) \\ y=3^{-x} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^{-x} \\ =0 or \infty \\ which is equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(C\right) \\ y=-3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }-3^x \\ =\infty or 0 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(D\right) \\ y=-3^{-x} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }-3^{-x} \\ =-\infty or 0 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(E\right) \\ y=3^x-1 \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^x-1 \\ =\infty or -1 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(F\right) \\ y=3^{x-1} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^{x-1} \\ =\infty or 0 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(G\right) \\ y=3^{1-x} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^{1-x} \\ =\infty or 0 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(H\right) \\ y=1-3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }1-3^x \\ =-\infty or 1 \\ which is not equal to y=0 \end{gathered}$$

$$\begin{gathered} \left(H\right) \\ y=1-3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }1-3^x \\ =-\infty or 1 \\ which is not equal to y=0 \end{gathered}$$