Question

Compare the functions below:

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

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:

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

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)