I have tried to resolve this problem but site shows error in my answer I have the fucntion $f(x)=1/x^2$
Use a graph to find the range of the function on the given interval below: $-3 \le x \le 3$.
Well, I do know the range doesn't exist for $0$ and my guess is that I have to get results between $-3$ and $3$, because I have $x^2$ the results will be positive so I think the solution should be $(0,9]$ or $0<x \le 9$ but the site says not correct.
Could you please help me with the problem? Thanks.
Jose
The question asks you to use a graph.
Have you tried looking at the graph of $y=f(x)$?
By examining the graph for our domain $-3 \leq x \leq 3$, it should be pretty clear that the range is $y \geq f(3)$ as the $y$ value never falls below $f(3)$ in our domain.
Remember that our function is $f(x) = \frac{1}{x^2}$, not $f(x) = {x^2}$. So $f(3)$ evaluates to $\frac{1}{9}$, not $9$.
Your range should also be given using $y$, not $x$, as the range represents a set of $y$ values.
Here's another way to think about it: consider what happens to $f(x)$ as $x$ approaches $0$. As $x$ becomes smaller, so does $x^2$. And fractions become larger in value as their denominators become smaller (for example, take $\frac{1}{0.01} = 100$). So as $x$ approaches $0$, $f(x)$ approaches infinity, i.e. $\lim_{x\to0} f(x) = \infty$.