SAT Nonlinear functions Practice Question 14 (Medium)

Math · Advanced MathMedium

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

$(-2, 3)$

$(3, 2)$

$(2, 3)$

$(2, -3)$

Show answer and explanation

Answer: C

The graph of $f$ has vertex $(0, 0)$ . Replacing $x$ with $x - 2$ shifts the graph 2 units right, and adding 3 shifts it 3 units up. So the vertex of $g$ is $(2, 3)$ .

Choice A shifts left because of the minus sign, but $f(x - 2)$ shifts the graph to the right.

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