Question

Use transformations to graph the equation$y=3e^x-2$.

Short answer

The graph is

Step-by-step solution

Step 1. Given Information

We are given the equation $y=3e^x-2$and we need to use transformations to graph it.

Step 2. Using transformations 

From the concept of the vertical and horizontal shift we know, the graph of $g\left(x\right)=f(x+c)+k$will be the graph of $f\left(x\right)$shifted left or right by $c$units depending upon the sign and up or down by $k$units depending upon the sign.

The graph of $g\left(x\right)=a.f\left(x\right)$produces a dilation and it will be the graph of $f\left(x\right)$stretched vertically if $a>1$.

Here the original function $y=e^x$is stretched vertically by $3$units and vertically shifting the graph down by$2$unis.

Step 3. Step 3. Plotting the graph 

The graph of the equation is