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f(x) = 3d(26x + 27) + 18 | SAT Linear functions Practice | Lumist

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Linear functions
f(x) = 3d(26x + 27) + 18

SAT Linear functions practice question

AlgebraMedium

$f(x) = 3d(26x + 27) + 18$

Which of the following represents the $x$ -intercept of the graph of $y = f(x) + 6$ in the $xy$ -plane, where $d$ is a constant?

Explanation

Set $f(x) + 6 = 0$ : $3d(26x + 27) + 18 + 6 = 0$ , so $3d(26x + 27) = -24$ , thus $26x + 27 = \dfrac{-24}{3d} = \dfrac{-8}{d}$ . Solving: $26x = \dfrac{-8}{d} - 27 = \dfrac{-8 - 27d}{d}$ , so $x = \dfrac{-8 - 27d}{26d} = \dfrac{-(8 + 27d)}{26d}$ . Multiplying numerator and denominator: this simplifies to match option B.

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