The function $f$ is defined as follows.
$$f(x)=\{\begin{array}{ll}3x& \text{ if }x\ne 0\\ 3& \text{ if }x=0\end{array}$$
(a) Find the domain of the function.
(b) Locate any intercepts.
(c) Graph the function.
(d) Based on the graph, find the range.
(e) Is $f$ continuous on its domain?

Step 1 ：The domain of the function is all real numbers because there are no restrictions on the values that x can take in the function $f(x)$.

Step 2 ：The y-intercept is at $(0,3)$ because when $x=0$, $f(x)=3$. The x-intercept is at $(1,3)$ because when $f(x)=0$, $x=1$.

Step 3 ：To graph the function, we plot the points $(0,3)$ and $(1,3)$ and draw a line through them. The line will be a straight line with a slope of 3, passing through the y-axis at $(0,3)$.

Step 4 ：Based on the graph, the range of the function is all real numbers because the line extends infinitely in both the positive and negative y-directions.

Step 5 ：The function $f$ is continuous on its domain because the function is defined for all real numbers and there are no breaks or jumps in the graph of the function.