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

It has amplitude of
`(1)/(4)`.

It is a horizontal shift of the parent function
`(\pi)/(3)` units left.

Explanation:

We have the function,
`f(x)=(1)/(4)\cos (x+(\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
`(1)/(4)`, which gives,
`\cos x => (1)/(4)\cos x`.

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

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

So, the correct options are,

It has amplitude of
`(1)/(4)`.

It is a horizontal shift of the parent function
`(\pi)/(3)` units left.