Back to Compare function properties — Problem 3 · Task Set 27

HSF.IF.C.9 Tutor Intake — Comparing Properties Across Representations

This short check helps your tutor understand where to start. Answer each question on your own. If you are not sure, give your best try — every response helps your tutor plan your sessions.

Grade 9·11 problems·~14 min·Common Core Math - HS Functions·group·hsf-if-c-9

Work through problems with immediate feedback

Concepts

Function A and Function B are two different functions. A student
observes that $f(3) > g(3)$ and concludes "Function A is always
greater than Function B." What is wrong with this reasoning?

Nothing — if one function is greater at one point, it is greater everywhere.

The comparison only shows that $f(3) > g(3)$ at a single input value.
The functions could cross or reverse order at other x-values.

The student should have compared $f(0)$ and $g(0)$ instead of at $x = 3$ .

The student needs to compare both functions at every integer to make a valid conclusion.