#### Answer

$\text{Domain: }
(-\infty,\infty)
\\\text{Range: }
(-\infty,\infty)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To graph the given linear function, $
g(x)=4x-1
,$ find two points on the line by identifying the $y$-intercept and the slope. Use the geometric interpretation of slope as $\dfrac{rise}{run}.$ Then use the graph to identify the domain and range of the function.
$\bf{\text{Solution Details:}}$
A linear function in the form $f(x)=mx+b,$ has a $y$-intercept of $b$ and a slope of $m.$ Since the $y$-intercept is $
-1
,$ the graph passes through $(0,
-1
).$ With a slope of $m=
4=\dfrac{4}{1}
=\dfrac{rise}{run}
,$ then from the $y$-intercept, move $
4
$ units up and then $
1
$ unit to the right to get the point $(
1,3
).$
Based on the graph the domain and range are as follows:
\begin{array}{l}\require{cancel}
\text{Domain: }
(-\infty,\infty)
\\\text{Range: }
(-\infty,\infty)
.\end{array}