SAT Nonlinear functions Practice Question 15 (Hard)

Math · Advanced MathHard

The function $f$ is defined by $f(x) = x^2 - 4x$ . The graph of $y = g(x)$ is the result of reflecting the graph of $y = f(x)$ across the $x$ -axis and then translating it up $5$ units. What is the maximum value of $g(x)$ ?

Student-produced response: enter your answer.

Show answer and explanation

Answer: 9

Completing the square, $f(x) = (x - 2)^2 - 4$ , so the minimum of $f$ is $-4$ . Reflecting across the $x$ -axis gives $-f(x)$ , which has maximum value 4. Translating up 5 gives $g(x) = -f(x) + 5$ , with maximum $4 + 5 = 9$ .

Reflecting the minimum to $-4$ instead of $4$ and then adding 5 gives the incorrect value 1.

Ask Owl about this question Next question

Got it wrong? On SAT Owl, Owl looks at the answer you chose and explains the exact mistake, then gives you similar questions until it sticks. Get your predicted SAT score free.