# functional equation

#### markdevin

##### New member
hello, i am having trouble solving these math problems. can someone help me?. I have to determine the functional equation of f and sketch a diagram in the coordination system. please look at the picture below.
Thank very much!

the diagram of a sine function f with f (x) = a * sin (kx) + b has the following properties: the function values are in the value range W (-8; 2). The distance between two high points is ^ (delta) x = π / 2. a) determine the functional equation of f. b) sketch the diagram in the coordinate system.

#### Dr.Peterson

##### Elite Member
Hi, Mark.

In order to help you most effectively, we ask you to show what work you can do, which helps us see where you need help.

The range of values lets you find a, the amplitude, and b, the vertical shift (which is the same as the "midline" for the graph).

The distance between successive high points tells you the period, which is related to k.

Does any of that sound familiar?

#### HallsofIvy

##### Elite Member
You know, I hope, that sin(x) has values between -1 and 1 so asin(x) has values between -a and a. And asin(x)+ b has values between b- 1 and b+ 1. sin(x) has period $$\displaystyle 2\pi$$ so sin(bx) has period $$\displaystyle \frac{2\pi}{b}$$.