Maryland Math F.IF.C.8.c

MathGrades 9–12INTERPRETING FUNCTIONS

The Standard

F.IF.C.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

Interpret the behavior of the graph of a function using the concept of limits.

Maryland College and Career Ready Standards for Mathematics (2025) · Analyze functions using different representations.

Teacher's field guide

What Students Need to Do: Students read a graph to tell what output values approach near a chosen input. They check both sides and distinguish the limit from the function's value at that input.
What Mastery Looks Like: A student can name the limit at a hole, even when a filled dot shows a different value. They can explain why a jump has no two-sided limit.
Common Misconceptions: Students may report the filled dot's value as the limit instead of looking at nearby points. They may give one limit at a jump without checking both sides.
How to Assess It: Exit ticket: Sketch y=2 for x<1 and y=4 for x>1, with f(1)=3. Give both one-sided limits and say whether the two-sided limit exists.

Lesson moves

On a coordinate grid, tape a horizontal strip at y=2 left of x=1 and another at y=4 right, then trace toward 1.
Draw y=x+1 with a hole at (2,3) and a filled dot at (2,5); ask why the limit differs from f(2).
Hand pairs four graph cards showing a hole, jump, vertical asymptote, and smooth curve; race to label each finite limit or no finite limit.
Graph a parking rate of $3 before noon and $5 from noon on; compare the rates approached just before and after noon.

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