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?

Can you explain your observations?

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

What do you notice this time?

Can you explain why the graphs behave in this way?