X and Y intercepts

Question

I have a function:

$$y =\begin{cases} 3x, &\text{if } x ≠ 0; \\ 4, & \text{if } x = 0. \end{cases}$$

As I understand, function doesn't exist at (0;0).
So, what are the intercepts?

Answer 1

If $f(0)=4$, then this is by definition the y-intercept.

For the x-intercept, you must solve for the case $f(x)=0$. Clearly, this is not the case for $x=0$, since $f(0)=4$. Then check $f(x)=3x=0$. This is only true for $x=0$. Thus, there is no x-intercept, it does not exist. For a line, it only intersects with the x-axis (At most) once. In the case of $b=0$, for $y=mx+b$, this is always at the origin of the graph. However, that doesn't work for this particular function, since it is defined differently at $x=0$.