SAT Linear functions Practice Question 15 (Hard)

Math · AlgebraHard

For the linear function $f$ , $f(x + 3) - f(x) = 12$ for all values of $x$ , and $f(0) = -2$ . What is the value of $f(5)$ ?

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Answer: 18

Increasing the input by 3 increases the output by 12, so the slope is $\frac{12}{3} = 4$ . With $f(0) = -2$ , $f(x) = 4x - 2$ . Then $f(5) = 20 - 2 = 18$ .

Treating 12 as the slope gives $f(5) = 58$ .

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