Answered

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

Sagot :

Given;

We are to reflect the function:

[tex]y=x^2\text{ -2}[/tex]

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

[tex]\begin{gathered} f(x)\text{ }\rightarrow\text{ -f'(x)} \\ \text{where the arrow represents the transformation} \end{gathered}[/tex]

Hence, the reflection of the given function gives:

[tex]\begin{gathered} y=f(x)=x^2\text{ -2} \\ f^{\prime}(x)=-(x^2-2) \\ =-x^2+2 \end{gathered}[/tex]

Thus the reflected function would be:

[tex]y^{^{\prime}}=-x^2+2[/tex]

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