Question

I would be one happy girl if you answered this for me!
Find a and d for the function
f(x) = a cos(x) + d such that the graph of f matches the figure.

Look at pic below :)

Answer 1

amplitude and period

Answer 2

looks like it is a regular cosine function(not shifted left or right) but instead of going from 1 to -1 it goes from \(9\) to \(-1\) a range of length \(10\)
that makes the amplitude \(5\)

Answer 3

ohh. so you add the above and the below.... I was saying that it was 9. haha thats wrong

Answer 4

what about the d in the equation?

Answer 5

yeah, that's wrong
so you know it is going to be \(y=5\cos(x)+d\)

Answer 6

is d the period?

Answer 7

you got to lift it up
no \(d\) is not the period

Answer 8

the period of cosine is \(2\pi\) as is the period of your function
you change the period via \(\cos(bx)\) but you don't need to change it here

Answer 9

you just have to raise it up a bit

Answer 10

right. right. right. so its 5cos(x) + 2pi

Answer 11

no

Answer 12

the number out at the end is NOT the period

Answer 13

you have to lift it up
lets go slow

Answer 14

the range has length \(10\) so the amplitude is \(5\)
if you had only \(y=5\cos(x)\) it would go from \(5\) to \(-5\) but you want to go from \(9\) to \(-1\)

Answer 15

in order to do that, you need to raise this sucker up 4 units
that gives you
\[y=5\cos(x)+4\]
the \(+4\) at the end lifts it up \(4\) units
now it goes from \(9\) to \(-1\) as desired

Answer 16

oh i see!! thanks for the explanation!!

Answer 17

yw
happy now?

Answer 18

http://www.wolframalpha.com/input/?i=5cos%28x%29%2B4
you can check the answer here