Learn on PengiBig Ideas Math, Advanced 2Chapter 6: Functions

Lesson 5: Section 6.5: Analyzing and Sketching Graphs

In this Grade 7 lesson from Big Ideas Math Advanced 2, Chapter 6, students learn to analyze and sketch graphs that show relationships between two quantities without relying on specific numerical values on the axes. Using real-world contexts like changing water levels, bike speeds, and city temperatures, students practice interpreting features such as steepness, increases, decreases, and plateaus to describe how one quantity changes relative to another. The lesson builds skills in matching situations to graphs and comparing graphs of scenarios like rocket launches and car speeds approaching traffic signs.

Section 1

Line Graphs

Property

Graphs are especially useful for illustrating the relationship between two variables. We could instead place a dot at the top of each bar. If we connect the dots with line segments, we have created a line graph. We often use line graphs to illustrate trends in data over time.

Examples

  • A line graph shows a student's test scores over a semester: 85 in September, 88 in October, 92 in November, and 90 in December. The line connecting these points shows a general improvement.
  • A line graph tracks the daily temperature for a week. The points might be 15∘C15^\circ C, 17∘C17^\circ C, 16∘C16^\circ C, 19∘C19^\circ C, 20∘C20^\circ C, 18∘C18^\circ C, and 17∘C17^\circ C. The line shows the temperature fluctuations.

Section 2

Analyzing Graph Behavior

Property

When analyzing a graph, we examine the overall behavior and relationships shown by the curve or line. This includes identifying patterns such as where the function increases or decreases, where it reaches maximum or minimum values, and how the rate of change varies across different intervals.

Examples

Book overview

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Chapter 6: Functions

  1. Lesson 1

    Section 6.1: Relations and Functions

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  2. Lesson 2

    Section 6.2: Representations of Functions

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  3. Lesson 3

    Section 6.3: Linear Functions

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  4. Lesson 4

    Lesson 4: Section 6.4: Comparing Linear and Nonlinear Functions

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  5. Lesson 5Current

    Lesson 5: Section 6.5: Analyzing and Sketching Graphs

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Lesson overview

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Section 1

Line Graphs

Property

Graphs are especially useful for illustrating the relationship between two variables. We could instead place a dot at the top of each bar. If we connect the dots with line segments, we have created a line graph. We often use line graphs to illustrate trends in data over time.

Examples

  • A line graph shows a student's test scores over a semester: 85 in September, 88 in October, 92 in November, and 90 in December. The line connecting these points shows a general improvement.
  • A line graph tracks the daily temperature for a week. The points might be 15∘C15^\circ C, 17∘C17^\circ C, 16∘C16^\circ C, 19∘C19^\circ C, 20∘C20^\circ C, 18∘C18^\circ C, and 17∘C17^\circ C. The line shows the temperature fluctuations.

Section 2

Analyzing Graph Behavior

Property

When analyzing a graph, we examine the overall behavior and relationships shown by the curve or line. This includes identifying patterns such as where the function increases or decreases, where it reaches maximum or minimum values, and how the rate of change varies across different intervals.

Examples

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 6: Functions

  1. Lesson 1

    Section 6.1: Relations and Functions

    LearnPractice
  2. Lesson 2

    Section 6.2: Representations of Functions

    LearnPractice
  3. Lesson 3

    Section 6.3: Linear Functions

    LearnPractice
  4. Lesson 4

    Lesson 4: Section 6.4: Comparing Linear and Nonlinear Functions

    LearnPractice
  5. Lesson 5Current

    Lesson 5: Section 6.5: Analyzing and Sketching Graphs

    LearnPractice