Question

Does a graph always have a y-intercept?

Answer 1

No.

Explanation:

Consider `f(x) = 1/x`
graph{1/x [-5, 5, -2.5, 2.5]}

Consider `g(x) = 1/x^2`
graph{1/x^2 [-5, 5, -0.2, 2.5]}

`lim_{x->0}1/x^2 = +infty`

Consider `h(x) = 2^(1/x)`
graph{2^(1/x) [-5, 5, -0.5, 2.5]}

It goes to zero, with a hole at (0,0).