Question

help Me Please!!!
Compare the functions below:


f(x)

x y
0 −5
1 0
2 3
3 4
4 3
5 0
6 −5
g(x) = 4 cos(2x − π) − 2 h(x) = −(x − 5)2 + 3


Which function has the largest maximum?

Answer 1

@aum hey you helped me before i was hoping you can help me again. :-)

Answer 2

For f(x) you can simply look at the table and find what the maximum y is.

g(x) = 4 cos(2x − π) − 2

What is the maximum value of a cosine function such as cos(x) or cos(2x − π)?

Answer 3

ok Hold on, let me work it out

Answer 4

No need to differentiate or graph the function. Remember the unit circle? What is the maximum a sine or a cosine function can attain?

Answer 5

would f(x) maximum value be 4?

Answer 6

yes.

Answer 7

Yay! so how do i do g(x)?

Answer 8

See my previous question.

Answer 9

so i would plug in the 4?

Answer 10

No. There are 3 different functions. You will have to find the maximum of each of the functions. You already found the max of f(x) to be 4. Next is to find the max of g(x). g(x) = 4 cos(2x − π) − 2. What is the max a cosine function can attain?

Answer 11

4

Answer 12

The max a cosine function can attain is 1.
The max 4 * cos(2x − π) can attain is 4 * 1 = 4
The max 4 cos(2x − π) − 2 can attain is 4 - 2 = 2

So the maximum value of g(x) is 2.

Answer 13

h(x) = −(x − 5)^2 + 3
This is the equation of a parabola in vertex form.
What is the vertex of this parabola?

Answer 14

will it be 3

Answer 15

-b/2(a)

Answer 16

vertex should have an x-coordinate and a y-coordinate.
Parabola in vertex form is: a(x-h)^2 + k where (h,k) is the vertex.
Compare this to −(x − 5)^2 + 3. What is (h.k)?

Answer 17

k is 3 and h is pi

Answer 18

so is the answer f(x)

Answer 19

h = 5, k = 3
The vertex is (5,3)
h(x) = −(x − 5)^2 + 3
is a vertical parabola that is upside down or opens downward and so it attains it maximum at the vertex. So the maximum value is the y-coordinate which is 3.

max value of f(x) is: 4
max value of g(x) is: 2
max value of f(x) is: 3

f(x) has the largest maximum value.

Answer 20

ohh wow you make it look so easy!! thanks so much! hey can you help me with maybe 2 more?

Answer 21

@aum