Question

Which transformation causes the described change in the graph of function $y=\cos \left(x\right)$?

The transformation results in horizontal stretch.

• A. $\frac{2}{7}\cos \left(x\right)$
• B. $-3\cos \left(x\right)$
• C. $\cos \left(7x\right)$
• D. $\cos \left(\frac{x}{3}\right)$

Answer 1

The correct option is D

$\cos \left(\frac{x}{3}\right)$

Explanation for the correct answer:

If the point $(x,y)$ shifted to $\left(kx,y\right)$ for some $\left|k\right|<1$, then we get it as horizontal stretch.

Given function $y=\cos \left(x\right)$.

Replacing $x$ by $kx$, we get $y=\cos \left(kx\right)$.

Let $k=\frac{1}{3}$ such that $\left|\frac{1}{3}\right|<1$.

$\therefore y=\cos \left(\frac{x}{3}\right)$

So, the transformation $\cos \left(\frac{x}{3}\right)$ results in horizontal stretch.

Hence, option $D$ is correct.