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:

$y^{^{\prime}}=-x^2+2$