How to find intersection with $x$ or $y$ axis As my question says, how do I find intersection with $x$ or $y$ axis.
For example, if given function is $f(x)=x^3+x^2-x-1$, how do I find the intersection with $x$ and $y$ axis.
Right now, I only know that when we are searching for intersection with $x$, we take $y=0$ and when we search for $y$, we take $x=0$.
However, if the intersection with $y$-axis, $x=0$, then we get, $f(x)=0+0-0-1$, therefore it will be, $(0,-1)$, but when we search for $x$-axis, $y=0$, what do change $0$ for? There is no $y$ in the function.
 A: Remember that $y=f(x)$, therefore saying $y=0$ is saying $f(x)=0$. So you just need to find $x$ such that $x^3+x^2-x-1=0$. To do this first inspect for pretty numbers like small (in absolute value) integers.
Below is the graph for your function (though that's probably what you're trying to find, I'm using it just as an illustrative example, I could have chosen a different function).
When does the graph intersect the $y$-axis? Exactly when $x=0$. And when does it intersect the $x$-axis? Exactly when $f(x)=0$.
Also take notice of Brian M. Scott's comment below, which is helpful.

By looking at the graph you can find that the points in which the graph intersects the $x$-axis are $(-1,0)$ and $(1,0)$ (note that the $y$ coordinate just had to be $0$, otherwise it wouldn't intersect the $x$-axis. Also looking at the graph you see that the point which intersects the $y$-axis is $(0,-1)$ (again, the $x$ component had to be $0$, otherwise it wouldn't intersect the $y$ axis).
Now let's confirm this fact algebraically:


*

*Find the intersection with the $x$-axis. Set $y=0$, that is $f(x)=0$. So you're trying to find $x$ such that $x^3+x^2-x-1=0$, which is equivalent to $(x-1)(x+1)^2=0$. So you get $x=1$ and $x=-1$ as roots of the equation. Since $y=0$, you get the intersecting points $(-1,0)$ and $(1,0)$, as expected.

*Find the intersection with the $y$-axis. Set $x=0$. You get $f(0)=y$ which is equivalent to $-1=y$. Therefore the point in which the graph of the function intersects the $y$-axis is $(0, -1)$.

A: For the Intersection with the $x$-axis you need to find the zeroes of the function, that means finding the $x$ which fulfulls $$0=x^3+x^2-x-1$$
Here x=1 should be one zero, and with polynomial division you should get the rest.
A: You're confused because you were being sloppy (or, because the question was stated sloppily). The question isn't asking about the intersection of a function with the x and y axes; it is asking about the intersection of the graph of that function with the x and y axes.
i.e. the question means to ask "what is the intersection of the curve defined by $y = f(x)$ with the x and y axes".
