Question

A sinusoidal function whose period is 1/2, maximum value is 10, and minimum value is -4 has a y-intercept of 3. What is the equation of the function described?

f(x)=7sin(4pix)+3
f(x)=7cos(4pix)+3
f(x)=7sin(4x)+3
f(x)=7cos(4x)+3

Answer 1

The period of the function is 1/2.

So first we need to find the argument of the function. The relation between the period and argument of a sinusoidal function is given by:

Period * Argument = 2πx

So,

Argument = 2πx / Period = 4πx

This means, the correct answer is either option A or B.

The y-intercept is 3. This means at x = 0, the value of function is 3.

Checking first option:
f(0) = 7 sin(0) + 3 = 3

Checking second option:
f(0) = 7cos(0) + 3 = 10

This means, only option A has the y-intercept at 3.

Therefore, the option which satisfies the given conditions is option A.

So, the correct answer is option A