Question

in the function f(x)=3x + 7, what is the input variable and what is the output variable?
a. using functional notation, the input variable is x and the output variable is y.

b. using functional notation, the input variable is f(x) and the output variable is x.

c. using functional notation, the input variable is f(x) and the output variable is y.

d. using functional notation, the input variable is x and the output variable is f(x).

Explanation:

In functional notation \( f(x) \), \( x \) is the input (the value we plug into the function), and \( f(x) \) represents the output (the result of applying the function to \( x \)). Option A incorrectly uses \( y \) instead of \( f(x) \) for output. Option B swaps input and output. Option C also swaps them. Option D correctly identifies \( x \) as input and \( f(x) \) as output.

Answer:

D. Using functional notation, the input variable is \( x \) and the output variable is \( f(x) \).