Question

Compare the functions

Answer 1

g(x) right? @freckles

Answer 2

let's play with it together

Answer 3

do you know the range of sin(x) is -1 to 1 ?

Answer 4

Well I'm thinking 2 spots on the number line from -1 to 1. lol

Answer 5

so one of the following will give the min to f
-3(-1)+2
-3(1)+2

so what is the min of f?



notice the parabola h is in vertex form
h=(x-h)^2+k where (h,k) is vertex
k gives the min value of the function

Answer 6

and given that what is also the min of h?

Answer 7

the function h

Answer 8

sorry I should have recalled the x-coordinate of the vertex something else

Answer 9

h=(x-c)^2+k where (c,k) is vertex
k gives the min value of this function

Answer 10

Ohh wait I totally read the question wrong! It asks for minimum, not maximum!

Answer 11

yep we want the smallest possible y per function

Answer 12

So f(x) is the greatest! Thank you :)

Answer 13

Wait no...hold on I'm redoing it.

Answer 14

you didn't answer my question
of the two numbers I mentioned above for f
can you tell me the smallest y value

Answer 15

really big hint:
\[-1 \le \sin(x- \pi) \le 1 \\ \text{ multiply both sides by -3 } \\ 3 \ge -3\sin(x-\pi) \ge -3 \\ \\ \text{ add 2 on both sides } 3+2 \ge -3\sin(x-\pi)+2 \ge -3+2 \]

Answer 16

Oh they're all the same? So it's D?

Answer 17

yes -3+2 is the min of f
and -1 is the min of g
and -1 is also the min of h

Answer 18

-3+2=-1=-1

Answer 19

Ohhh okay! Thank you so much! :)