Question

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? (6 points)
Select one:
a. f(x)
b. g(x)
c. h(x)
d. All three functions have the same maximum value.

Answer 1

`f(x)\to y_(max)=4\\\\g(x)=4\cos(2x-\pi)-2\to y_(max)=2\\\\h(x)=-(x-5)^2+3\to y_(max)=3`

Answer: a. f(x)

Answer 2

Option: a is the correct answer.

a. f(x)

Explanation:

• We are given a set of values for the function f(x) as:

x y =f(x)

0 −5

1 0

2 3

3 4

4 3

5 0

6 −5

Clearly from the set of values we could observe that:

The maximum value of the function f(x) is: 4

• Now we are given function g(x) as:

`g(x)=4 \cos(2x-\pi)-2`

We know that maximum value of g(x) is attained when the cosine function attains the maximum value.

Also the maximum value of cosine function is: 1

Hence, the maximum value of g(x) is : 4-2=2

• Now we are given a quadratic function h(x) as:

`h(x)=-(x-5)^2+3`

As we know that the function:

`(x-5)^2\geq 0\\\\This\ implies\ that:\\\\-(x-5)^2\leq 0\\\\-(x-5)^2+3\leq 3`

Hence, the maximum value of function h(x) is: 3

Hence, the function that has the largest maximum is:

f(x) ( which is 4)