3.1 Functions and function notation  (Page 5/21)

To evaluate $h\left(4\right),$ we substitute the value 4 for the input variable $p$ in the given function.

Therefore, for an input of 4, we have an output of 24.

If $\left(p+3\right)\left(p-1\right)=0,$ either $\left(p+3\right)=0$ or $\left(p-1\right)=0$ (or both of them equal 0). We will set each factor equal to 0 and solve for $p$ in each case.

This gives us two solutions. The output $h\left(p\right)=3$ when the input is either $p=1$ or $p=-3.$ We can also verify by graphing as in [link] . The graph verifies that $h\left(1\right)=h\left(-3\right)=3$ and $h\left(4\right)=24.$

To express the relationship in this form, we need to be able to write the relationship where $p$ is a function of $n,$ which means writing it as $p=[\text{expression}\text{involving}n].$

Therefore, $p$ as a function of $n$ is written as

First we subtract $x^2$ from both sides.

We now try to solve for $y$ in this equation.

We get two outputs corresponding to the same input, so this relationship cannot be represented as a single function $y=f\left(x\right).$ If we graph both functions on a graphing calculator, we will get the upper and lower semicircles.