Chapter 3.1, Problem 14E

To determine

To match: The given exponential function with the correct graph.

Answer to Problem 14E

The equation $f\left(x\right)=2^x+1$ is matched to graph $\left(\text{c}\right)$ .

Explanation of Solution

Given information:

The exponential function $f\left(x\right)=2^x+1$ . The given graphs are:

  

Calculation:

Consider the provided function $f\left(x\right)=2^x+1$ . Construct a table with different values of x .

Substitute $x=-1$ in the above function.

  $\begin{array}{c}f\left(-1\right)=2^{-1}+1\\ =\frac{1}{2}+1\\ =\frac{3}{2}\end{array}$

Substitute $x=0$ in the above function.

  $\begin{array}{c}f\left(0\right)=2^0+1\\ =1+1\\ =2\end{array}$

Substitute $x=1$ in the above function.

  $\begin{array}{c}f\left(1\right)=2^1+1\\ =2+1\\ =3\end{array}$

Substitute $x=2$ in the above function.

  $\begin{array}{c}f\left(2\right)=2^2+1\\ =5\end{array}$

The above obtained values are tabulated as,

  $\begin{array}{ccccc}x& -1& 0& 1& 2\\ f\left(x\right)& \frac{3}{2}& 2& 3& 5\end{array}$

It is observed that the graph of the function passes through the point $\left(0,2\right)$ . The graph of the equation is an increasing function of x since as values of x increases the corresponding value of the function $f\left(x\right)=2^x+1$ increases.

Thus, from all the graphs, the equation is matched to graph $\left(\text{c}\right)$ .