SAT Linear functions Practice Question 20 (Hard)

Math · AlgebraHard

$x$	$f(x)$
$-1$	$k$
$3$	$10$
$7$	$3k$

The table shows three values of $x$ and their corresponding values of $f(x)$ , where $f$ is a linear function and $k$ is a constant. What is the value of $f(0)$ ?

$\frac{5}{4}$

$5$

$\frac{25}{4}$

$\frac{15}{2}$

Show answer and explanation

Answer: C

The $x$ -values are equally spaced by 4, so the outputs must change by equal amounts: $10 - k = 3k - 10$ , giving $k = 5$ . The outputs are 5, 10, 15, so the slope is $\frac{5}{4}$ . Then $f(0) = f(-1) + \frac{5}{4} = 5 + \frac{5}{4} = \frac{25}{4}$ .

Choice B is $f(-1)$ , the value of $k$ , rather than $f(0)$ .

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