Question

Let the function f(x) have the form f(x) = Acos(x+C). To produce a graph that matches the one shown below, what must the value of A be?
(graph to be added)
a) 2
b) 3
c) 4
d) 1

Answer 1

what is the midline in this case?

Answer 2

i really have no idea

Answer 3

alright, how about the highest and lowest points

Answer 4

the y values (I don't care about the x values)

Answer 5

4

Answer 6

y = 4 and what else

Answer 7

y = 4 corresponds to the max

Answer 8

-4

Answer 9

y = -4 is the min, yes

Answer 10

now find the distance from the max y = 4 to the min y = -4

Answer 11

8?

Answer 12

good, then we finally cut that in half to get the amplitude

Answer 13

so the amplitude is 4

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the alternative way is to find the midline

add up the max and min and then divide by 2

(4 + (-4))/2 = (4-4)/2 = 0/2 = 0

the midline is y = 0

then find the distance from the midline to the max, that is 4 units (same as the distance from the midline to the min). So this is another way to get the amplitude to be 4.

Answer 14

oh so its 4? thats it??

Answer 15

correct

Answer 16

either way, you're going to get 4

Answer 17

thank you so much, can you help me on one more?

Answer 18

sure

Answer 19

for the function y= -2+5 sin (pi/12(x-2)) what is the minimum value?

Answer 20

what is the range of sin(x) ?

Answer 21

all real numbers between -1 and 1?

Answer 22

good

Answer 23

so if you multiply EVERY output possible that comes out of sin(x)

and you multiply the outputs by 5, what is the new range?

Answer 24

In other words

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

\[\Large a \le 5\sin(x) \le b\]

what goes in place of 'a' and 'b' ?

Answer 25

pi and 12?

Answer 26

you agree that \[\Large -1 \le \sin(x) \le 1\] right?

Answer 27

right

Answer 28

we can multiply every part of that inequality by 5

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

\[\Large 5*(-1) \le 5\sin(x) \le 5*1\]

\[\Large -5 \le 5\sin(x) \le 5\]

Answer 29

so 5sin(x) is in between -5 and 5

Answer 30

with me so far?

Answer 31

actually yeah

Answer 32

so the smallest that 5*sin(x) can get is -5

this is true no matter what x is, so you can replace x with any crazy complicated expression you want and -5 will still be the min

Answer 33

however

Answer 34

we have a -2 hanging out front

Answer 35

so -2+5sin(x) will have a min of -2+(-5) = -7

and again, you can replace x with whatever you want and that min won't change