Question

If a funtion f is periodic and has a period of 3/4, and if f(1)=2, give two other values of x, one positive and one negative, such that f(x)=2.

Answer 1

The sine and cosine functions are the most common periodic functions. Have you considered using one or the other as your model?

If you choose either the sine or the cosine function, the basic form of the first would be

y=a*sin(bx) + c.

b is regarded as the frequency; a the amplitude, and c the vertical offset.

Experiment with this model. Try to figure out what value b will have if the actual period is 3/4. The relevant equation is \[period=\frac{ 2 \pi }{ b }\]

Answer 2

"if f(1)=2" states that if x takes on the value 1, the function y=f(x) takes on the value 2.
Find two other x values, such that the value of the function is also 2 at both.

Answer 3

Hint: The starting value of x is 1. That comes from "if f(1)=2," above.
What would x=1 become were y ou to add the period to it? were you to subtract the period from it?

Answer 4

So I just subtract 3/4 from 1 and add it as well?

Answer 5

pretty much, yes

because, if we know that f(1) = 2, means, that when x = 1, y =2
and on the next period around, that is, 3/4 later or earlier, it will go back to 2
because is PERIODic, or comes back to its old rhythm

Answer 6

Ohhh, I understand now. Thank you!

Answer 7

yw