Question

Graphing Exponential Functions Graph the function, not by plotting points, but by starting from the graphs in Figure 2.

State the domain, range, and asymptote.

$\mathit{g}\mathbf{\left(}\mathit{x}\mathbf{\right)}\mathbf{=}{\mathbf{2}}^{\mathbf{x}}\mathbf{-}\mathbf{3}$

(Figure – 2)

Short answer

The graph is:

The domain is $(-\infty ,\infty )$.

The range is $(-3,\infty )$.

The horizontal asymptote is $y=-3$.

Step-by-step solution

Step-1 – Given 

The given function is $g\left(x\right)=2^x-3$.

Step-2 – To determine

We have to sketch a graph for the given function using figure 2. Then we have to state its domain, range and asymptote.

Step-3 – Calculation

$y=-3$The parent function of $g\left(x\right)=2^x-3$is $y=2^x$.

To get the graph of $g\left(x\right)=2^x-3$from $y=2^x$we’ll move the function $y=2^x$by 3 units down.

So, the graph will be:

From the graph, we see the possible values ofx are all real numbers. So, the domain is.

They-values are from$-3$ to $\infty$. So, the range is .

And the horizontal asymptote of the graph is.