SAT Math formula sheet · all 24 · Advanced Math · #12 of 24

Function transformations on the SAT: How It Is Tested

Nonlinear functions

Transformations diagram for the SAT: They only really test you on shifts. Vertical, think outside. Horizontal, think inside. Vertical is intuitive: f(x) + 5
What it is really testingThey only really test you on shifts. Vertical, think outside. Horizontal, think inside. Vertical is intuitive: f(x) + 5 means up 5. Horizontal is counterintuitive: f(x + 5) means left 5, not right 5.

The question from the sheet

Hard
SAT Advanced Mathanswer C
The function ff is defined by the given equation. The function gg is defined by g(x)=f(x+3)g(x) = f(x + 3). For what value of xx does g(x)g(x) reach its minimum?
f(x)=3x2+42x+150f(x) = 3x^{2} + 42x + 150
A-7
B-3
✓-10
D-4

How the diagram applies

  1. Find where ff has its minimum first: x=−b2a=−426=−7x = -\dfrac{b}{2a} = -\dfrac{42}{6} = -7.
  2. g(x)=f(x+3)g(x) = f(x + 3): inside the parentheses, so it moves the OPPOSITE way. Plus 33 shifts the graph LEFT 33.
  3. The minimum moves from x=−7x = -7 to x=−10x = -10.

Answer: C

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Common Questions

It comes up as an SAT nonlinear functions question. They only really test you on shifts. Vertical, think outside. Horizontal, think inside. Vertical is intuitive: f(x) + 5 means up 5. Horizontal is counterintuitive: f(x + 5) means left 5, not right 5.

Find where f has its minimum first: x = -b2a = -426 = -7. g(x) = f(x + 3): inside the parentheses, so it moves the OPPOSITE way. Plus 3 shifts the graph LEFT 3. The minimum moves from x = -7 to x = -10.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Transformations is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.