Question

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

The transformation __ results in vertical stretch.

• A. $\frac{1}{3}\cos \left(x\right)$
• B. $\cos \left(x+4\right)$
• C. $\cos \left(-5x\right)$
• D. $-5\cos \left(x\right)$

Answer 1

The correct option is D

$-5\cos \left(x\right)$

Explanation of the correct answer:

When a point $\left(x,y\right)$ on the graph of the function $y=f\left(x\right)$ shifts to $\left(x,y_1\right)$ on the graph of the function $y_1=kf\left(x\right)$, for $\left|k\right|>1$ then there is a vertical shift in the graph.

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

Replace $\cos \left(x\right)$ by $k\cos \left(x\right)$, we get $y=k\cos \left(x\right)$.

Let $k=-5$ such that $\left|-5\right|>1$.

$\therefore y=-5\cos \left(x\right)$

So, the transformation $-5\cos \left(x\right)$ results in vertical stretch.

Hence, option $D$ is correct.