Question

What are the domain, period, range, and amplitude of the function graphed? Will post a picture of the graph in the comments. Please help!

Answer 1

If I did it right, I think the amplitude is 0.75.

Answer 2

So, let's look at the amplitude first. The amplitude is how far away from the center line the wave can extend (at the peaks). This wave is centered at 0. It extends up to 1/2, and down to -1/2. So what is the amplitude?

Answer 3

The amplitude would be 0.75.

Answer 4

Not quite. Another way to get the amplitude is it's (maximum value - minimum value) divided by 2

Answer 5

That's what I did. (0.5-(-0.5))/2 = 0.75

Answer 6

Try that again :)

Answer 7

0.5 - (-0.5) = 0.5 + 0.5 = ?

Answer 8

Ohh right. Lol. 1

Answer 9

divided by 2 = 1/2

So your amplitude is 1/2

Answer 10

Now, the period is the "distance" from two identical points on the wave. Peak to peak, for instance. What is that for this wave?

Answer 11

4?

Answer 12

By distance, do you just mean the number of units in between each peak?

Answer 13

It's 4 units, correct. But those units each equal a certain number of radians, in this graph. You'd need to convert.

An easier way may be to take the locations of the peaks an subtract them (their x components), as this also finds the distance between them.

Answer 14

How do I convert to radians? I got the (6, 0) - (2, 0) = (4, 0) like you said.

Answer 15

See the
\[\frac{\pi}{2}\]
on the second line to the right of the y axis? That means that 2 units = pi/2 radians.
We can use that to convert from 4 units to the corresponding number of radians.

Answer 16

So if pi/2 is 2 units, I would multiply pi/2 by pi/2? If so, I got 2.47 radians.

Answer 17

\[\frac{\pi}{2} radians = 2 units\]
\[=> \frac{\pi}{4} radians = 1 unit\]

So how many radians in 4 units?

Answer 18

8 radians?.. This is confusing. If pi/2 radians is 2 units, I don't get why pi/4 is only 1 unit.

Answer 19

If pi/2 = 2 units, we just divide by the number of units (2, in this case) to see how many each unit is worth.

pi/2 = 2 units
divide both sides by 2:
pi/4 = 1 unit

so:
4 units = 4*(pi/4) radians = pi

Answer 20

Oh okay.. So the period is just pi or 3.14?

Answer 21

Yep :)

Answer 22

So, the "domain" is just a fancy word for the values that you can put into a function (usually called "x") and get an answer out.

Is there any number that we CAN'T put in for x and get an answer back out?

Answer 23

No? The x values are 1, 3, 5 and 7

Answer 24

Those are the "zeroes" of the function, but you are correct. We can put in any number we want, and the function gives us an answer for it.

So, the domain is "all real numbers"

Answer 25

The range is the fancy term for the interval of answers that are possible to get. That is, if a function can give answers between the numbers 1 and 2 (including those numbers), then the range is: [1,2]

Answer 26

So would the range for this one be [-0.5, 0.5]?

Answer 27

There ya go :)

If you have other, similar problems, try to do them just like we did here. How we went about it was pretty general.

Answer 28

I have all of this written down because it's definitely the best I've seen it explained. Easiest for me to learn anyway! Thanks so much for helping. :)

Answer 29

My pleasure :)