These functions are available as cards if you would like to try to match some of them up with the sketch graphs.

Please note that we haven’t included a set of possible input values with the equations for the functions because this is one of the things that you need to think about. In each case you should think about what the graph of the function might look like if it were sketched for all possible input values of \(x.\)

How many roots does \(g(x)\) have?

Where does \(h(x)\) change sign? Where is \(h(x)\) positive and where is it negative?

What can you say about \(p(x)\) when \(x\) is a long way from \(0\)?

What do the two parts of \(q(x)\) look like? How does \(q(x)\) behave close to \(x=7\)?

How many times does \(r(x)\) change sign?

How does \(s(x)\) behave when \(x\) gets very large?