The function $f$ is defined as follows. \[ f(x)=\left\{\begin{array}{ll} 3 x & \text { if } x \neq 0 \\ 3 & \text { if } x=0 \end{array}\right. \] (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.