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Common Core Math8th GradeFunctions

8.F.2: Compare Functions in Different Forms

Also written as 8.F.A.2 and CCSS.MATH.CONTENT.8.F.A.2 · Cluster: Define, evaluate, and compare functions.

Make an 8.F.2 WorksheetAll 28 8th Grade Math Standards

The Official Wording

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change.

Common Core State Standards, Grade 8, Functions · Read it at the source · Checked October 14, 2026

What 8.F.2 Means in Plain English

Eighth graders compare two functions that arrive in different forms. Gym A is a sentence: $30 to join, then $15 a month. Gym B is a table: 1 month costs $32, 3 months cost $68. Students find B’s rate, $18 a month, and see it climbs faster.

The same comparison runs between a graph and an equation, or a verbal rule and a graph, and covers starting values as well as rates. High school widens it to any two functions shown in different ways, quadratics and exponentials included (HSF-IF.9).

8.F.2 I Can Statements

  • I can find the rate of change from a table, graph or equation.
  • I can find the starting value of a function in any form.
  • I can say which of two functions grows faster, and prove it.

8.F.2 Worked Example

Two phone plans, one as a table and one as an equation, where the cheaper start belongs to the plan that climbs faster.

Problem

Plan A charges by this table: 0 GB costs $20, 2 GB costs $26, 4 GB costs $32. Plan B charges y = 4x + 15 dollars for x GB of data. Which plan’s cost goes up faster, and which one starts higher?

Which phone plan’s cost grows faster?
  1. In the table, divide the change in cost by the change in data between two rows.Plan A: (26 − 20) ÷ (2 − 0) = 6 ÷ 2 = $3 per GB
  2. In y = mx + b the rate is the number multiplying x, and b is the cost at 0 GB.Plan B: y = 4x + 15, so $4 per GB
  3. Starting values: read the x = 0 row of the table, and the b of the equation.Plan A starts at $20, Plan B at $15
  4. B starts $5 lower but climbs $1 more per GB, so at some point it catches up with A. Set the two costs equal to find where.4x + 15 = 3x + 20, so x = 5 GB
AnswerPlan B’s cost grows faster, $4 per GB against $3, even though Plan A starts higher, $20 against $15. They cost the same at 5 GB.

Check it: Test the table’s other pair: (32 − 26) ÷ (4 − 2) = 3, so A’s rate holds. At 5 GB, A costs 20 + 3 × 5 = $35 and B costs 4 × 5 + 15 = $35.

Common Mistakes with 8.F.2

Reading the rate off one row

Plan A: 26 ÷ 2 = $13 per GB

Try this: Subtract two rows first: change in cost over change in data. Dividing one output by its input ignores the $20 starting fee.

Comparing the starting values instead

“Plan A grows faster because $20 is more than $15.”

Try this: Separate the two questions: the starting value says where a function begins, the rate says how fast it climbs. Answer each one apart.

Taking the constant as the rate

y = 4x + 15 read as “a rate of 15”

Try this: Circle the number attached to x before anything else. That coefficient is the change per unit, and the lone 15 is the starting value.

Where 8.F.2 Fits

Comes Before7.RP.2Find the unit rate in a table, graph or equation of a proportional relationship.8.EE.5Compare two proportional relationships, like a graph against an equation.
Alongside8.F.1Know that a function gives exactly one output for each input.8.F.3Recognize y = mx + b as a linear function whose graph is a line.
Comes Next8.F.4Build a linear function from a description, a table or two points.
HSF-IF.9Compare any two functions shown in different ways, nonlinear ones included.

Practice 8.F.2

Math Worksheet GeneratorFree ToolPairs of linear functions, one as a table and one as an equation, with a line under each pair to name the faster rate, and an answer key.Rate of changeTable vs equationAnswer key
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Quick Check

  1. Function A is y = 2x + 7. Function B is a table with (1, 5), (3, 11), (5, 17). Which has the greater rate of change?
  2. One candle starts 20 cm tall and burns down 1.5 cm an hour. Another’s height is h = 24 − 2t. Which burns faster, and which starts taller?
  3. A graphed line passes through (0, 3) and (2, 9). Is its rate of change greater or smaller than that of y = 2.5x + 3?

8.F.2: Other Names

8.F.28.F.A.2CCSS.MATH.CONTENT.8.F.A.2

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.