Question

Which of the following statements are true about the graph of f (x) = 1/4 coz ( x + π/3) - 1? Select all that apply.

Answer 1

Answer:

It has amplitude of $\frac{1}{4}$.

It is a horizontal shift of the parent function $\frac{\pi}{3}$ units left.

Step-by-step explanation:

We have the function, $f(x)=\frac{1}{4}\cos (x+\frac{\pi}{3})-1$.

It is clear that the parent function is $g(x)=\cos x$.

So, we see that,

The amplitude of the function f(x) is $\frac{1}{4}$, which gives, $\cos x => \frac{1}{4}\cos x$.

Also, g(x) is translated $\frac{\pi}{3}$ units to the left, which gives, $\frac{1}{4}\cos x => \frac{1}{4}\cos (x+\frac{\pi}{3})$.

Further, the function is translated 1 unit downward, resulting in $f(x)=\frac{1}{4}\cos (x+\frac{\pi}{3})-1$.

So, the correct options are,

It has amplitude of $\frac{1}{4}$.

It is a horizontal shift of the parent function $\frac{\pi}{3}$ units left.