CCSS.Math.Content.8.F.A

CCSS.Math.Content.8.F.A is a cluster heading. These are the individual standards under it.

• CCSS.Math.Content.8.F.A.1

  Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input a...

• CCSS.Math.Content.8.F.A.2

  Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• CCSS.Math.Content.8.F.A.3

  Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear.

01

What Students Need to Do

Students decide whether each input has exactly one output. They find outputs for given inputs and identify rates, starting values, and patterns from tables, graphs, equations, or descriptions. They compare relationships shown in different forms.

02

What Mastery Looks Like

Students correctly decide whether a table, graph, mapping, or equation represents a function. They evaluate outputs and compare rate of change, starting value, and graph shape across different representations.

03

Common Misconceptions

Students may think repeated outputs mean a relation is not a function. They may swap inputs and outputs, read graph scales incorrectly, or compare starting values instead of rates of change.

04

How to Assess It

Give students the table x: 0, 1, 2 and y: 3, 5, 7, then compare it with y = 3x + 1. Ask which has the greater rate of change and how they know.

1. 01

   Give pairs input and output cards, then have students build mappings and check whether each input connects to exactly one output.

2. 02

   Ask students to explain why repeated outputs can still make a function, but one input paired with two outputs cannot.

3. 03

   Run a matching game where students pair tables, graphs, equations, and descriptions that represent the same function.

4. 04

   Compare two phone plans using a table and equation, then choose the cheaper plan for different amounts of monthly data.

• CCSS.Math.Content.HSF-IF.A.2

  Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

• CCSS.Math.Content.HSF-IF.C.9

  Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

• CCSS.Math.Content.HSF-IF.C

  Analyze functions using different representations