For the function F(X) = 3|X| - 5, what is F(-7)?

To find ( F(-7) ) for the function ( F(X) = 3|X| - 5 ), you begin by substituting (-7) into the function in place of (X):

1. Calculate the absolute value of (-7):

[

| -7 | = 7

]

2. Substitute this value back into the function:

[

F(-7) = 3| -7 | - 5 = 3(7) - 5

]

3. Multiply (3) by (7):

[

3 \times 7 = 21

]

4. Now subtract (5) from (21):

[

21 - 5 = 16

]

Thus, ( F(-7) = 16 ). The value of (F(-7)) is correctly calculated as (16). This corresponds with the function evaluation processes and how absolute values work, ensuring the output reflects the function’s behavior with negative input values, ultimately leading to the correct answer.