The function f is defined by f(x) = x^2 - 6x + 8. The graph... | SAT Nonlinear functions Question, Answer Explained

Math · Advanced MathMedium

The function $f$ is defined by $f(x) = x^2 - 6x + 8$ . The graph of $y = g(x)$ is the result of shifting the graph of $y = f(x)$ to the left $2$ units. Which equation defines $g$ ?

$g(x) = x^2 - 10x + 24$

$g(x) = x^2 - 6x + 6$

$g(x) = x^2 - 6x + 10$

$g(x) = x^2 - 2x$

Show answer and explanation

Answer: D

Shifting a graph left $2$ units replaces $x$ with $x + 2$ : $g(x) = f(x + 2) = (x + 2)^2 - 6(x + 2) + 8 = x^2 + 4x + 4 - 6x - 12 + 8 = x^2 - 2x$ . Check: the vertex of $f$ is $(3, -1)$ and the vertex of $g$ is $(1, -1)$ .

Choice A replaces $x$ with $x - 2$ , which shifts the graph to the right instead of the left.

Why the other choices are wrong

A. This is f(x - 2), which shifts the graph 2 units to the right.
B. This subtracts 2 from f(x), which shifts the graph down 2 units.
C. This adds 2 to f(x), which shifts the graph up 2 units.

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, or take a free full-length practice test.