if f is a linear function and f(3) = 7, which of the following could be the definition of f?

Question

a) f(x) = -x + 10

b) f(x) = -x^2 + 16

c) f(x) = x^2 - 2

d) f(x) = 2x + 2

Answer 1

all are correct, except d

Answer 2

Hi Theodore!

Happy to help you answer this.

The question is asking us to use 3 as a specific input, which has an output of 7 to find a possible function (something with an input and an output) that could produce that result. There are an infinite number of possible functions that could have an input of 3 and an output of 7, so we'll have to go through each of the answer choices to find a match.

A)

f(x) = -x +10

f(3) = -(3) + 10

f(3) = 7

So our first answer choice a is a correct answer.

Let's check the other answer choices to see if there are any additional correct answers. Or, at a minimum, to see what it looks like when an answer choice isn't correct.

B)

f(x) = -x² + 16

f(3) = -(3)² + 16

f(3) = -9 + 16

f(3) = 7

So, b is also a correct answer.

C)

f(x) = x² - 2

f(3) = (3)² - 2

f(3) = 9 - 2

f(3) = 7

Seeing as the output is 7 when the input is 3 here, c is another correct answer.

D)

f(x) = 2x + 2

f(3) = 2(3) + 2

f(3) = 6 + 2

f(3) = 8

With a result of 8 instead of 7, d cannot be a correct answer.

In summary, answer choices a, b, and c are all possible definitions of the function.