Image and preimage of a function 
Given the function $f(x)=x^{2}-4x-5$, $A=[0,3)$ and $B=[0,1]$, find $f(A)$ and $f^{-1}(B)$.

I found $f(A)$ by looking at the graph $f([0,3))=[-9,-5]$  but how would I calculate this without the graph? If I plug in $0$ into $f$ I get $-5$, and if I plug in $3$ I get $-8$, when I should get $-9$.

More general if $f: \mathbb{R} \rightarrow \mathbb{R}, f(x) = ax^2 + bx + c, a \gt 0$ then $f$ is decreasing on $(-\infty, - \frac b {2a}]$ and increasing on $[- \frac b {2a}, + \infty)$. You can use this together with the fact that $f$ is continuous to get the images you want.
