Hello!
The y-intercept of a function is the point of intersection of the graph of this function and the y-axis. So such a point belongs both to y-axis and to the graph of a function.
All points on the y-axis have an x-coordinate of 0, they are of the form `(0, y),` where `y` may be any number.
All points on the graph of a function `f(x)` have the form `(x, f(x)),` where `x` is any number from the domain of `f.`
If both conditions are met, we have `x = 0` and the second coordinate is `f(0),` hence the y-intercept of `f` is the point `(0, f(0)),` it is unique if function is one-valued. Of course this requires that `0` is in the domain of `f,` otherwise `f` has no y-intercept.
For example, `f(x)= x^2+1` has the y-intercept `(0, 1),` and `g(x) = 1/x` has no y-intercept.
More general curves, not graphs of (one-valued) functions, may have more than one y-intercept, for example the circle `x^2+y^2=1` has two (find them yourself using `x=0` ).
No comments:
Post a Comment