SAT Function Notation and Nonlinear Graphs

Function notation questions ask you to evaluate, compose or transform functions, and to read nonlinear graphs. Expressions such as f(x + 1) − f(x) require both terms — computing the first and forgetting the subtraction is the standard slip.

Practise this skill freeHow the SAT is structured
MathAdvanced Math98 questions
The trap on this skill

Expanding f(x + 1) but forgetting to subtract the original f(x).

How this skill behaves

What 98 questions on it look like

89% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

43% of the bank for this skill is rated hard, so it rewards practice past the point where the basic form feels comfortable.

medium46%
hard43%
easy11%

Difficulty mix across the 98 questions in this skill.

From the bank

Three real function notation and nonlinear graphs questions

Each one explains the credited answer and why every other option fails.

Advanced Math · medium

A function used in the readingnook weekday scanner packing entry card is f(x) = 3x^2 + 2x - 5. Which expression is equivalent to f(x + 1) - f(x)?

  1. A3x + 2
  2. B6x + 2
  3. C6x + 5correct
  4. D3x^2 + 6x + 0
Why C is correct — and why the others are not

Compute f(x + 1) = 3(x + 1)^2 + 2(x + 1) - 5. Subtracting f(x) leaves 6x + 5. The final step answers the prompt as it applies to Function notation and nonlinear graphs. A final check is following the order of operations in the displayed expression.

A. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

B. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

D. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

Advanced Math · easy

A function used in the observatory weekend badge counting batch card is f(x) = 4x^2 + 3x - 5. Which expression is equivalent to f(x + 1) - f(x)?

  1. A4x + 3
  2. B8x + 3
  3. C4x^2 + 8x + 2
  4. D8x + 7correct
Why D is correct — and why the others are not

Compute f(x + 1) = 4(x + 1)^2 + 3(x + 1) - 5. Subtracting f(x) leaves 8x + 7. The key support is the way the item treats Function notation and nonlinear graphs. A final check is checking the requested variable before recording the answer.

A. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

B. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

C. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

Advanced Math · hard

A function used in the dockside outdoor handle scanning stock card is f(x) = 3x^2 + 5x - 5. Which expression is equivalent to f(x + 1) - f(x)?

  1. A3x + 5
  2. B6x + 8correct
  3. C6x + 5
  4. D3x^2 + 6x + 3
Why B is correct — and why the others are not

Compute f(x + 1) = 3(x + 1)^2 + 5(x + 1) - 5. Subtracting f(x) leaves 6x + 8. The calculation or reading check points back to Function notation and nonlinear graphs. A final check is confirming that the answer form matches the prompt.

A. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

C. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

D. This value results from expanding f(x + 1) but forgetting to subtract the original f(x)

98 questions on this skill, free to start.

Ten a day at no cost, each with the same explanation. One account covers SAT, ACT and AP.

Start free
FAQ

Function Notation and Nonlinear Graphs questions

What does f(x + 1) mean?

Substitute x + 1 wherever x appears in the rule. It is not f(x) + 1.

How do graph transformations work?

Changes inside the function move the graph horizontally and in the opposite direction to the sign; changes outside move it vertically in the direction of the sign.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Quadratic Functions and Equations135 questionsNonlinear Equations in One Variable127 questionsEquivalent Expressions120 questionsExponential Functions and Equations113 questions

Practise function notation and nonlinear graphs until the trap stops working.

Real Digital SAT questions, the reasoning on every option, and a mistake bank that only clears when you get it right.

Start freeSAT guide