Question

In the following exercises, match the graphs to one of the following functions:

$ⓐ2^xⓑ2^{x+1}ⓒ2^{x-1}ⓓ2^x+2ⓔ2^x-2ⓕ3^x$

Short answer

The correct match is,$\left(a\right)2^x$.

Step-by-step solution

Step 1 Given functions are,

$ⓐ2^xⓑ2^{x+1}ⓒ2^{x-1}ⓓ2^x+2ⓔ2^x-2ⓕ3^x$

The given graph is,

The objective is, we need to find the function which should matches with the given graph.

Step 2 From the graph it is clear that the graph is of an increasing function.

So, the standard form of the function is,$f\left(x\right)=a^x\left[a>1\right]$

From the graph it is very clear that the point $\left(1,2\right)$is on the graph.

So, $$\begin{gathered} 2=a^1 \\ a=2 \end{gathered}$$

We know that $f\left(x\right)=a^x$.

So,$f\left(x\right)=2^x$.

So, the correct match is,$\left(a\right)2^x$.