molly compared the function (f(x)= - 4sin(x)) to the absolute - value function (g(x)) shown in this…
molly compared the function (f(x)= - 4sin(x)) to the absolute - value function (g(x)) shown in this table.\n| (x) | (g(x)) |\n|----|----|\n| - 4 | 2 |\n| - 3 | 4 |\n| - 2 | 6 |\n| - 1 | 4 |\n| 0 | 2 |\nwhat is the sum of the maximum values of (f(x)) and (g(x))?\na. 2\nb. 4\nc. 6\nd. 10
Answer
Explanation:
Step1: Determine the maximum value of $f(x)$.
The function is $f(x) = -4\sin(x)$. The range of the sine function, $\sin(x)$, is $[-1, 1]$. To find the maximum value of $f(x)$, we multiply the range of $\sin(x)$ by $-4$. The minimum value of $f(x)$ occurs when $\sin(x) = 1$: $f(x) = -4(1) = -4$. The maximum value of $f(x)$ occurs when $\sin(x) = -1$: $f(x) = -4(-1) = 4$. So, the maximum value of $f(x)$ is $4$.
Step2: Determine the maximum value of $g(x)$ from the table.
The table provided for $g(x)$ is:
| x | g(x) |
|---|---|
| -4 | 2 |
| -3 | 4 |
| -2 | 6 |
| -1 | 4 |
| 0 | 2 |
| The values of $g(x)$ listed in the table are $2, 4, 6, 4, 2$. | |
| The maximum value of $g(x)$ from this table is $6$. |
Step3: Calculate the sum of the maximum values of $f(x)$ and $g(x)$.
The sum of the maximum values is the maximum value of $f(x)$ plus the maximum value of $g(x)$. Sum = Maximum value of $f(x)$ + Maximum value of $g(x)$ Sum = $4 + 6$ Sum = $10$
Answer:
D. 10