Answer
(a) domain $(-\infty,\infty)$
(b) no $x$-intercept; $y$-intercept is $1$
(c) Refer to the attached image.
(d) range $(-\infty,0)\cup(0,\infty)$
(e) not continuous
Work Step by Step
Based on the given piece-wise function, we have:
(a) The domain is the set of all values of $x$.
Thus, the domain of the given function is $(-\infty,\infty)$ since no $x$ value is excluded.
(b) To find the $x$-intercepts, let $f(x)=0$ then solve for $x$:
$2x=0\\
x=0$
This contradicts the definition of the given function which says $f(0)=1$, thus the function has no $x$-intercept.
To find the $y$-intercepts, let $x=0$:
$f(0)=1$
Thus, the $y$-intercept is $1$.
(c) The graph of the function is the $y=2x$ except when $x=0$ where $f(x)=y=1$.
Thus, the graph is a line with a hollow dot at $x=0$, and the point $(0, 1)$.
Refer to the graph below.
(d) The range of the function is the set of all $y$ values.
The graph shows that the $y$ value can be any real number except $0$.
Thus, the range is $(-\infty,0)\cup(0,\infty)$.
(e) We can see that $f(x)$ is not continuous on its domain as there is a discontinuity at $x=0$.
