Why can a function have multiple x-intercepts but only one y-intercept?

Answer 1

It can, but only if the line drawn is a curve.

----------------------------------------------------------------------------------

The function is a polynomial of the form:

y = f(x) = a{0} + a₁x + a₂x² + a₃x³ + ...... a{n}xⁿ = Σa{i}xⁱ for i = 0, 1, 2, 3, ..., n

(Note a{r} is my way of writing "a subscript r", eg a{1} = a₁, and each a{n} is the coefficient of the xⁿ term.)

The x-intercept is where y = 0 and there are n values of x for which the polynomial's value is 0 (some of which may be complex values, eg f(x) = x² + 1 has solutions for f(x) = 0 where x = ±i).

However to be a function there must only be one y value for each x value (there can be more than one instance of any y value, ie there can be more than one x value that have the same y value, eg y = x² has y = 4 for x = ±2). Thus there will only be one y value for x = 0, ie only one y-intecept.