Question

How does changing the function from f(x) = −5 cos 2x to g(x) = −5 cos 2x − 3 affect the range of the function?

The function shifts down 3 units, so the range changes from −1 to 1 in f(x) to −4 to −2 in g(x).
The function shifts down 3 units, so the range changes from −5 to 5 in f(x) to −8 to 2 in g(x).
The function shifts down 5 units, so the range changes from −1 to 1 in f(x) to −6 to −4 in g(x).
The function shifts down 5 units, so the range changes from −5 to 5 in f(x) to −10 to 0 in g(x).

Answer 1

@phi @radar @aloud @AutumnRoseT @xavierbo2 @Data_LG2 @mathmate @HWBUSTER00 @hartnn

Answer 2

was up

Answer 3

help mee?

Answer 4

i really d know

Answer 5

okay thanks though

Answer 6

@mathmate ?

Answer 7

@georgia545 @aloud
Do you know the range of f(x)?

Answer 8

0??

Answer 9

So the range of y=cos(x) is [-1,1]
Are you familiar with the interval notation?

Answer 10

noo

Answer 11

Check this out:
http://www.coolmath.com/algebra/07-solving-inequalities/03-interval-notation-01

Answer 12

oh yeah i do i just didnt know that was the name

Answer 13

range of y=[-1,1] means the range of y can take any value between -1 and +1.

Answer 14

Multiplying y by -5 means stretching the function vertically and flipping it about the x-axis.
so y=-5cos(x) has a shape like this:

so what is the range of y=-5cos(x)?