Question

Question 5

What is the equation of the following graph?

f(x) = 2cos x

f(x) = 3cos x


f of x equals one-half times cosine of x


f of x equals one-third times cosine of x

Answer 1

Hello!

Firstly, you can notice that this graph has a range of
`-1/2 \leq y \leq 1/2`. Amplitude is the maximum displacement on the graph of a function, and it can be determined if it is located on the front of a function. It's like a vertical stretch, it located on the front of function, but different.

If y = A cos x , then the amplitude is |A|. Note this is the absolute value of A. For a limited domain, the value of A would determine the maximum height of these functions. Therefore, the amplitude is 1/2.

Therefore, the only function that has a amplitude of 1/2 is choice C, f of x equals one-half times cosine of x or f(x) = 1/2cos(x).