Question

For the function y= -1+6cos(2pi/7(x-5)) what is the maximum value?

(sorry I keep asking so many questions)

Answer 1

cosine is a lot like sine in many ways (hence the name coSINE)

cosine has a range from -1 to 1, ie,

\[\Large -1 \le \cos(x) \le 1\]

Answer 2

use the same idea used last time and hopefully you see how to find the range of the entire function

Answer 3

oh, so -6<cos<6?

Answer 4

more like

\[\Large -6 \le 6\cos(x) \le 6\]

Answer 5

oh

Answer 6

therefore the max of the piece "6cos(2pi/7(x-5))" is 6

that is the largest output you can get from that piece

Answer 7

so what is the overall max?

Answer 8

6? or so we have to do something with the -1?

Answer 9

yeah that -1 will change things

Answer 10

so is it -6?

Answer 11

-1 + 6 = 5 actually

Answer 12

the -1 pulls the graph down 1 unit

Answer 13

taking the max down 1 unit as well

Answer 14

ohh

Answer 15

so the answer is five?

Answer 16

correct

Answer 17

thank you again!!