CCSS.Math.Content.HSF-IF.C.9
The Standard
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Common Core State Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find the same key features of two functions shown in different forms. They compare those features and justify which function has the greater value, rate, maximum, or minimum.
What Mastery Looks Like
- Students accurately find intercepts, rates of change, maxima, minima, and intervals from different representations. They make a correct comparison and support it with a value, coordinate, or feature.
Common Misconceptions
- Students may compare how graphs look without checking axis scales. They may confuse a maximum with a y-intercept, compare outputs at different inputs, or overlook domain restrictions.
How to Assess It
- Display a downward-opening graph of f with vertex (2, 9) and give g(x) = -2(x + 1)^2 + 7. Ask which function has the larger maximum and what evidence proves it.
Lesson moves
Ways to Teach It
Give pairs cards showing equations, graphs, tables, and descriptions, then have students identify and compare one shared feature for each pair.
Ask students to explain why a steeper-looking graph may not have a greater rate of change when the axis scales differ.
Play Function Face-Off, where pairs draw representation cards and earn a point by correctly comparing a named property.
Compare two phone plans shown as a table and an equation, then decide which costs less at three given usage levels.
Free download
Printable HSF-IF.C.9 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSF-IF.C.9, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.8.F.A.2
The high school target repeats the same comparison skill with more advanced functions and representations, so the grade 8 skill directly carries over.
- CCSS.Math.Content.8.F.A.1
Comparing functions across tables, graphs, formulas, and words requires understanding inputs, outputs, and graph points as paired values.
- CCSS.Math.Content.HSF-IF.B.4
Interpreting key features in graphs, tables, and descriptions supports comparing those same features across two differently represented functions.
What This Unlocks
Mastery here sets students up for these next.
Keep exploring
Related Standards
- CCSS.Math.Content.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or ...
- CCSS.Math.Content.HSF-IF.C.8
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- CCSS.Math.Content.8.F.A
Define, evaluate, and compare functions.
Turn this exact standard into a lesson
Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.