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Pre-Algebra Functions (introductory)

Interpreting graphs of functions

20 practice questions 0 video lessons Theory + worked examples

Interpreting Graphs of Functions

California Pre-Algebra • Standard 8.F.5 • Functions

Interpreting Graphs of Functions is a topic in Functions in the California Common Core State Standards. It is aligned to Standard 8.F.5, which requires students to interpret and describe the qualitative features of function graphs.

A graph tells a story: rising means increasing, flat means constant, falling means decreasing, and steepness shows the rate.

California Pre-Algebra › Functions › Interpreting Graphs of Functions  —  Standard 8.F.5

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Theory

Reading a graph describes how a quantity changes over the input:
  • Rising: increasing.
  • Flat: constant.
  • Falling: decreasing.
Steeper sections change faster.
Interpreting a graph A graph's shape shows where a quantity increases, stays constant, or decreases. time increasing constant decreasing
Increasing, constant, decreasing.
Reading graphs Reading graphs Reading graphs rising: increasing flat: constant falling: decreasing steeper: faster change
Reading a graph's shape.

Shape and meaning:

\[\text{slope}>0\ \text{up},\ =0\ \text{flat},\ <0\ \text{down}\]
positive slope rises, zero slope is flat, negative slope falls
A qualitative graph shows the story without numbers.

How to interpret a graph

  1. Scan left to right along the input.
  2. Note where it rises, flattens, or falls.
  3. Compare steepness for speed of change.
  4. Describe the story in words.
Example 1 — Increasing
What does a rising section of a graph mean?
Solution

The quantity is increasing over time.

the quantity is increasing
Example 2 — Constant
What does a flat section mean?
Solution

The quantity stays constant.

the quantity is constant
Example 3 — Decreasing
What does a falling section mean?
Solution

The quantity is decreasing.

the quantity is decreasing
Example 4 — Steepness
What does a steeper slope indicate?
Solution

A faster rate of change.

a faster rate of change

Common pitfalls

Flat does not mean zero — it means unchanging.
Steeper means faster, not higher.
Read left to right over the input.

Frequently asked questions

What does a rising graph mean?

The quantity is increasing.

What does a flat graph mean?

The quantity is constant.

What does steepness show?

How fast the quantity changes.

What does a falling graph mean?

The quantity is decreasing.

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