Review question

# Can we identify the right sketch of a product of functions? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R8749

## Solution

On which of the axes below is a sketch of the graph $y = 2^{-x} \sin^2 (x^2)?$

• Both $2^{-x}$ and $\sin^2(x^2)$ are functions that are never negative, so $y\geq0$, which discounts b.

• At $x=0$, $2^{-x} = 1$ and $\sin^2 (x^2)=0$, so $y(0)=0$, which discounts d.

• Finally, the graph meets the $x$-axis when $\sin^2 (x^2) = 0$, which occurs when $\sin (x^2)=0$, so at

$x = \sqrt{\pi}, \sqrt{2\pi}, \sqrt{3\pi}, \ldots.$

These are not evenly spaced as in c. These values get closer together as $x$ increases, as in a.