Maryland Math F.IF.A.2.a

MathGrades 9–12INTERPRETING FUNCTIONS

The Standard

F.IF.A.2: Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Extend evaluating functions to include operations with composite functions, e.g. f(x + 2) − f(x).

Maryland College and Career Ready Standards for Mathematics (2025) · Understand the concept of a function and use function notation.

Teacher's field guide

What Students Need to Do: Students substitute a number or expression, such as x+2, into a function rule. They can also use one function's output as another function's input, then combine the results as directed.
What Mastery Looks Like: Given f(x)=x² and g(x)=x+2, a student finds f(g(x))=(x+2)² and simplifies f(x+2)-f(x) to 4x+4. They use parentheses when substituting and know which function to apply first.
Common Misconceptions: Students may treat f(x+2) as f(x)+2 or expand (x+2)² as x²+4. Some treat f(g(x)) as multiplication instead of using g(x) as the input to f.
How to Assess It: Exit ticket: Let f(x)=x²+1. Find and simplify f(x+2)-f(x), and show what you substituted into f.

Lesson moves

Give pairs cards labeled f(t)=t², t=x, and t=x+2; have them place each input into the rule and subtract the results.
Show f(x)=x² and two claims, f(x+2)=x²+4 and f(x+2)=x²+4x+4; ask which is correct and why.
Run a function-machine race with f(x)=2x-1 and g(x)=x+3; teams compute f(g(2)) and g(f(2)).
Set a taxi fare at C(m)=4+2m dollars; ask students what C(m+2)-C(m) means and calculate it.

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