Question

A. Reflect y = x^2 – 2 across the x-axis.

Answer 1

Given;

We are to reflect the function:

`y=x^2\text{ -2}`

Given a function f(x), the rule for reflecting across the x-axis is:

`\begin{gathered} f(x)\text{ }\rightarrow\text{ -f'(x)} \\ \text{where the arrow represents the transformation} \end{gathered}`

Hence, the reflection of the given function gives:

`\begin{gathered} y=f(x)=x^2\text{ -2} \\ f^(\prime)(x)=-(x^2-2) \\ =-x^2+2 \end{gathered}`

Thus the reflected function would be:

`y^{^(\prime)}=-x^2+2`