Why can a function have on more than one Y-intercept?

Question

but the X-intercept can have more than one

Answer 1

A function is defined as an input output system (for lack of a better word) which produces exactly 1 y value for each x value. So if the "function" crosses the y-axis in more than one place, there are at least 2 values of y for x=0. This means that it cannot be a function. There are, however, no restrictions on the amount of x values for a given y-value (say y=0).

Answer 2

Because the definition of a function is: for every value of the independent variable x there is at most one value for the dependent variable y. This means that if it IS a FUNCTION and x=0 (thus the y axis) then there is only ONE value for y (the y intercept). But in the case of a non linear function such as a parabola (lets say y=x^2 - 25 (that is y=x squared - 25)) , there are 2 values (x=5 and x= -5) where y=0 and these are then of course on the x axis, thus x intercepts,but only one place where
x=0 and this is at y= -25, the only y intercept

Answer 3

The main reason is because if y had more than one y-intercept, then it wouldn't be a function.

Recall that a function has to pass the vertical line test. If we have two y-intercepts, (which we'll call a and b), then the graph goes through the points (0, a) and (0, b).

What then, is f(0)? Remember that a function maps ONE value to another, and here we have f(0) mapping to TWO values; a and b. Such a graph would not be a function (it would be a relation).

Answer 4

If it is not a linear function it can have many y intercepts

Take x^2+y^2-25=0 and put x=0 y=+-5(two y intercepts)
If you put y=0 you get x=+-5 (two x intercepts)

Answer 5

If it is a function, then for each value of x, there is only one possible value of y. That's what function means. Given a value of x, you have a formula or method that gives you the corresponding value for y.

This means that for x = 0, there is only one possible value for y. If there was more than one value, it wouldn't be a function.

On the other hand, two different values of x might have the same value of y.

For example, when you drive from New York to Chicago, your height above sea level changes as you go along the freeway. The height is a function of the distance along the freeway. So at any particular distance, you'll only be at one height above sea level - you won't be at two different heights at the same time. But there might be two different places along the freeway where you were at a particular height, say 100 feet above sea level.

Answer 6

if there are two y-int, that means there are two outputs with x =0. it is not a function when there is 1 input to 2 outputs.

x int is where a line cross the x-xis.

Quadratic function has two x-int
cubic has three
and so on

Answer 7

There is only one possible y-int for a linear equation.
There is only one possible x-int for a linear equation.

On the other hand, if a line is something like:
y = x^2 + 3
Then it would have multiple y-intercepts.
The first would be 3 and then it would eventually loop back.
I hope that helped.

Answer 8

Otherwise, using the vertical line test, a vertical line would cross the graph more than once and it would no longer be a function, but only a relation.

Answer 9

a function doesn't repeat values - in other words - for every x value there is a y value, but no two y values can have the same x value otherwise it wouldn't be a function