Tayarri SAT
Math, Advanced Math, Stage 3

Functions on the SAT: lesson and practice

f(a) means "substitute a for x". f(g(x)) means apply g first, then f. For transformations, changes inside the bracket move the graph horizontally in the opposite direction, and changes outside move it vertically in the same direction.

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TransformationEffect on point (p, q)
f(x − 3)right 3: (p + 3, q)
f(x) + 2up 2: (p, q + 2)
−f(x)reflect over x-axis: (p, −q)
f(−x)reflect over y-axis: (−p, q)

Composition

f(x) = 5x + 8, g(x) = 2x + 4
g(2) = 8, then f(8) = 48

Common mistakes

Treating f(a) + f(b) as f(a + b)Evaluate each separately.
Composing in the wrong orderf(g(x)): inside first.
Shifting the wrong wayf(x − 3) moves right, not left.

Sample questions with answers

1. If f(x) = 7x − 8, what is f(5) + f(−2)?
  1. 13
  2. 5 (correct)
  3. 27
  4. −594

f(5) = 27 and f(−2) = −22; the sum is 5.

2. (−5, 5) is on y = f(x). Which point is on y = f(x + 4) + 3?
  1. (−1, 8)
  2. (−9, 2)
  3. (−9, 8) (correct)
  4. (−2, 1)

x + 4 moves left 4; + 3 moves up 3.

3. If f(x) = 5x + 8 and g(x) = 2x + 4, what is f(g(2))?
  1. 40
  2. 48 (correct)
  3. 144
  4. 8

g(2) = 8 and f(8) = 48.

Frequently asked questions

How are functions tested on the SAT?

Through function notation, composition, graphs and transformations. Advanced Math makes up about 35% of SAT Math, roughly 13 to 15 questions.

What does f(x − h) do to a graph?

It shifts the graph h units to the right.

How do I evaluate f(g(x))?

Find g(x) first, then substitute the result into f.

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