Chapter 1.3, Problem 10E

Solution

To match: the given graph with its function and verify with graphing window $\left[-4.7,4.7\right]\times \left[-3.1\times 3.1\right]$ .

The graph matches with option (c) $y=e^x-2$ .

Given information: The given graph is,

  

Formula used:

The graph of the function $y=f\left(x\right)-k$ is found by shifting the graph of the function $y=f\left(x\right)$ by $k$ units downward.

Calculation:

See the shape of the graph.

The graph resembles to the graph of $y=e^x$ .

Consider the basic function $y=e^x$ .

Shift the graph 2 unit to downward such that the $y$ -intercept is $-2$ .

Thus, the graph of the function is $y=e^x-2$

The given graph matches with option (c).

Graph the function in the graphing window $\left[-4.7,4.7\right]\times \left[-3.1\times 3.1\right]$, by using graphing calculator:

  

Hence, the graph matches with option (c) $y=e^x-2$ .