Select the correct answer from the drop-down menu. Find the maximum value of each function.
| x | -5 | -4 | -3 | -2 | 0 | 1 | 2 | 3 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| f(x) | -7 | 0 | 5 | 8 | 8 | 5 | 0 | -7 |
The maximum value of [tex]f(x)[/tex] is $\square$ the maximum value of [tex]g(x)[/tex].
Answer (2)
Identify the values of f ( x ) from the table.
Determine the maximum value of f ( x ) , which is 8.
Note that g ( x ) is not defined, so a comparison is not possible.
The maximum value of f ( x ) is 8.
Explanation
Understanding the Problem We are given a table of x and f ( x ) values and asked to find the maximum value of f ( x ) and compare it to the maximum value of g ( x ) . However, g ( x ) is not defined, so we can only find the maximum value of f ( x ) .
Finding the Maximum Value of f(x) From the table, the values of f ( x ) are -7, 0, 5, 8, 8, 5, 0, -7. The maximum value is 8.
Comparison with g(x) Since g ( x ) is not defined, we cannot compare the maximum value of f ( x ) with the maximum value of g ( x ) . However, we can say that the maximum value of f ( x ) is 8.
Final Answer The maximum value of f ( x ) is 8. We cannot compare it to the maximum value of g ( x ) because g ( x ) is not defined in the problem.
Examples
Imagine you are tracking the daily high temperatures in a city over a period of time. The function f ( x ) represents the high temperature on day x . Finding the maximum value of f ( x ) tells you the hottest temperature recorded during that period. This information can be useful for planning purposes, such as preparing for heat waves or determining the peak demand for air conditioning.
The maximum value of the function f ( x ) is 8, which occurs at x = − 2 and x = 0 . There is no information given about g ( x ) , so a comparison cannot be made. Therefore, the focus remains solely on the maximum value of f ( x ) , which is 8.
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