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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.

Respuesta :

gmany
[tex]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[/tex]

Answer: a. f(x)

Answer:

Option: a is the correct answer.

a.  f(x)

Step-by-step 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:

[tex]g(x)=4 \cos(2x-\pi)-2[/tex]

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:

[tex]h(x)=-(x-5)^2+3[/tex]

As we know that the function:

[tex](x-5)^2\geq 0\\\\This\ implies\ that:\\\\-(x-5)^2\leq 0\\\\-(x-5)^2+3\leq 3[/tex]

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

             Hence, the function that has the largest maximum is:

                        f(x)  ( which is 4)

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