Question

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

Short answer

(D)$y=-3^{-x}$

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:

$$\begin{gathered} \left(A\right) \\ y=3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^x \\ =\infty or0 \\ whichisnotequaltoy=0 \end{gathered}$$

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

$$\begin{gathered} \left(C\right) \\ y=-3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }-3^x \\ =\infty or0 \\ whichisnotequaltoy=0 \end{gathered}$$

$$\begin{gathered} \left(D\right) \\ y=-3^{-x} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }-3^{-x} \\ =-\infty or0 \\ whichisequaltoy=0 \end{gathered}$$

$$\begin{gathered} \left(E\right) \\ y=3^x-1 \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^x-1 \\ =\infty or-1 \\ whichisnotequaltoy=0 \end{gathered}$$

$$\begin{gathered} \left(F\right) \\ y=3^{x-1} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^{x-1} \\ =\infty or0 \\ whichisnotequaltoy=0 \end{gathered}$$

$$\begin{gathered} \left(G\right) \\ y=3^{1-x} \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }{3}^{1-x} \\ =\infty or0 \\ whichisnotequaltoy=0 \end{gathered}$$

$$\begin{gathered} \left(H\right) \\ y=1-3^x \\ li{m}_{x\to \pm \infty }y=li{m}_{x\to \pm \infty }1-3^x \\ =-\infty or1 \\ whichisnotequaltoy=0 \end{gathered}$$