SAT Nonlinear functions Practice Question 18 (Hard)

Math · Advanced MathHard

The function $f$ is defined by $f(x) = x^2 + 2x - 8$ . The function $g$ is defined by $g(x) = f(x + 3)$ . What is the sum of the $x$ -coordinates of the $x$ -intercepts of the graph of $y = g(x)$ ?

$-8$

$-2$

$2$

$4$

Show answer and explanation

Answer: A

Factor: $f(x) = (x + 4)(x - 2)$ , so $f$ has zeros at $-4$ and $2$ . The graph of $g(x) = f(x + 3)$ is the graph of $f$ shifted 3 units left, so its zeros are $-7$ and $-1$ . Their sum is $-8$ .

Choice D shifts the zeros 3 units right (to $-1$ and $5$ ) instead of left.

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