Comparing Two Functions

Free

Grades 8–9AlgebraGuided journey: Discover, Learn, Practice, Apply

Compare two linear or nonlinear rules in the same context: read which function starts higher, grows faster, or matches first; use tables, graphs, and $f(x)$ notation; and interpret break-even points where two models tie.

What you’ll learn

Compare functions by evaluating the same input in both rules; larger output wins at that input only.
Linear starting values appear as $y$ -intercepts; rates appear as slopes in $y=mx+b$ .
Equal outputs solve like a system: set the two expressions equal and solve for the input.
Tables and shared graphs make tie points and intervals of dominance visible before algebra.
Context units matter: compare dollars to dollars, miles to miles, not mixed labels.

Aligned to 8.F.A.2

Comparing Two Functions

Free

Grades 8–9AlgebraGuided journey: Discover, Learn, Practice, Apply

What you’ll learn

Compare functions by evaluating the same input in both rules; larger output wins at that input only.
Linear starting values appear as $y$ -intercepts; rates appear as slopes in $y=mx+b$ .
Equal outputs solve like a system: set the two expressions equal and solve for the input.
Tables and shared graphs make tie points and intervals of dominance visible before algebra.
Context units matter: compare dollars to dollars, miles to miles, not mixed labels.

Aligned to 8.F.A.2