Answer
domain: $(-\infty, +\infty)$
range: $(-\infty, +\infty)$
Refer to the graph below.
Work Step by Step
Find the x-intercept by setting $f(x)$ or $y$ to zero, then solve for $x$.
$f(x) = 3x
\\0=3x
\\\frac{0}{3}=\frac{3x}{3}
\\0=x$
The x-intercept is $(0, 0)$.
Find the y-intercept by setting $x=0$ then solving for $y$.
$f(x)=3x
\\f(x) = 3(0)
\\f(x)=0$
The y-intercept is $(0, 0)$.
Since the x and y-intercepts are the same, one more point is needed to graph the linear function. This can be found by assigning any value to $x$ then solving for $y$:
If $x=2$,
$f(2) = 3(2)
\\f(2) = 6$
Thus, the point $(2, 6)$ is also on the line.
Plot $(0, 0)$ and $(2, 6)$ and connect the points using a line to complete the graph.
(Refer to the graph in the answer part above.)
The graph covers all x-values and all y-values.
Thus, the given function has:
domain: $(-\infty, +\infty)$
range: $(-\infty, +\infty)$
