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 $x$.
$f(x) = -2x
\\0=-2x
\\\frac{0}{-2}=\frac{-2x}{-2}
\\0=x$
The x-intercept is $(0, 0)$.
Find the y-intercept by setting $x=0$ then solving for $y$.
$f(x)=-2x
\\f(x) = -2(0)
\\f(x)=0$
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 $x=1$,
$f(1) = -2(1)
\\f(1) = -2$
Thus, the point $(1, -2)$ is also on the line.
Plot $(0, 0)$ and $(1, -2)$ 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: $(-\infty, +\infty)$
