Combining Functions

Package of problems

Problem

Sketch the graph of $y=\dfrac{1}{x+a}$ for different values of $a$. We suggest you start by trying the values $a=0$, $1$, $-1$.

What do you notice?

Now sketch the graph of $y=\dfrac{1}{x^2+a}$ for different values of $a$, again starting with $a=0$, $1$, $-1$.