Review question

# Can we pick the graph of $y=\sin^2{\sqrt{x}}$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6656

## Solution

The graph of $y=\sin^2{\sqrt{x}}$ is drawn in

The function $y=\sin^2{\sqrt{x}}$ is positive for any positive $x$, so it cannot be (a).

The local maximum of $y=\sin^2{\sqrt{x}}$ is $1$ for $\sqrt{x} = \left(\dfrac{\pi}{2}\right), \left(\dfrac{3\pi}{2}\right), \left(\dfrac{5\pi}{2}\right) ...$, so it cannot be (c) as its first two local maxima are of different values.

And the frequency of our function is not constant, as it is in the case of $\sin x$. We can see this by looking at the $x$ values of the first few maxima: $x = \dfrac{\pi^2}{4}, \dfrac{9\pi^2}{4}, \dfrac{25\pi^2}{4}...$

These are not equally separated, so it cannot be (d).

Which means the correct answer is (b).