Taking it further

Here are some more functions for you to think about.

• How would you start to sketch graphs of these functions? What are the key features you would look out for?

• Is there a reasonable sketch of any of these functions in the sketch graphs from the main part of the problem?

\begin{align*} g(x)&=\dfrac{7}{(x+5)(x-3)}\\ & \\ h(x)&=\dfrac{5-x}{(x+1)(x-6)}\\ & \\ p(x)&=\dfrac{(x-2)^2}{(x+2)(x-4)}\\ & \\ q(x)&=\begin{cases}(6-x)(x+1) & \text{if } x <7\\ \dfrac{8}{x-8} & \text{if } x \geq 7 \end{cases}\\ & \\ r(x)&=\dfrac{x-3}{(x+1)^{2}(x-6)^{2}}\\ & \\ s(x)&=x-3+\dfrac{25-11x}{x^2-3x+5} \end{align*}

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 $x.$