Learn on PengiBig Ideas Math, Algebra 1Chapter 4: Writing Linear Functions

Lesson 7: Piecewise Functions

Property.

Section 1

Definition and Notation of Piecewise Functions

Property

A piecewise function is defined by different equations over different intervals of its domain. The general notation is:

f(x)={equation1if condition1equation2if condition2⋮⋮equationnif conditionnf(x) = \begin{cases} \text{equation}_1 & \text{if condition}_1 \\ \text{equation}_2 & \text{if condition}_2 \\ \vdots & \vdots \\ \text{equation}_n & \text{if condition}_n \end{cases}

Examples

Section 2

Determining Domain Conditions for Piecewise Functions

Property

For a piecewise function f(x)={f1(x)if x satisfies condition 1f2(x)if x satisfies condition 2⋮⋮f(x) = \begin{cases} f_1(x) & \text{if } x \text{ satisfies condition 1} \\ f_2(x) & \text{if } x \text{ satisfies condition 2} \\ \vdots & \vdots \end{cases}, determine which piece applies by checking which condition the input value satisfies.

Examples

Section 3

Evaluating Piecewise Functions

Property

To evaluate a piecewise function at a given input value, first determine which piece (or condition) the input satisfies, then substitute the input into the corresponding function rule for that piece.

Examples

Section 4

Graphing Piecewise Functions

Property

To graph a piecewise function, we plot each piece separately on its specified domain, then combine them into one graph. Each piece is graphed only over its defined interval, and we use open or closed circles to indicate whether endpoints are included.

Examples

Book overview

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

Continue this chapter

Chapter 4: Writing Linear Functions

  1. Lesson 1

    Lesson 1: Writing Equations in Slope-Intercept Form

    LearnPractice
  2. Lesson 2

    Lesson 2: Writing Equations in Point-Slope Form

    LearnPractice
  3. Lesson 3

    Lesson 3: Writing Equations of Parallel and Perpendicular Lines

    LearnPractice
  4. Lesson 4

    Lesson 4: Scatter Plots and Lines of Fit

    LearnPractice
  5. Lesson 5

    Lesson 5: Analyzing Lines of Fit

    LearnPractice
  6. Lesson 6

    Lesson 6: Arithmetic Sequences

    LearnPractice
  7. Lesson 7Current

    Lesson 7: Piecewise Functions

    LearnPractice

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Definition and Notation of Piecewise Functions

Property

A piecewise function is defined by different equations over different intervals of its domain. The general notation is:

f(x)={equation1if condition1equation2if condition2⋮⋮equationnif conditionnf(x) = \begin{cases} \text{equation}_1 & \text{if condition}_1 \\ \text{equation}_2 & \text{if condition}_2 \\ \vdots & \vdots \\ \text{equation}_n & \text{if condition}_n \end{cases}

Examples

Section 2

Determining Domain Conditions for Piecewise Functions

Property

For a piecewise function f(x)={f1(x)if x satisfies condition 1f2(x)if x satisfies condition 2⋮⋮f(x) = \begin{cases} f_1(x) & \text{if } x \text{ satisfies condition 1} \\ f_2(x) & \text{if } x \text{ satisfies condition 2} \\ \vdots & \vdots \end{cases}, determine which piece applies by checking which condition the input value satisfies.

Examples

Section 3

Evaluating Piecewise Functions

Property

To evaluate a piecewise function at a given input value, first determine which piece (or condition) the input satisfies, then substitute the input into the corresponding function rule for that piece.

Examples

Section 4

Graphing Piecewise Functions

Property

To graph a piecewise function, we plot each piece separately on its specified domain, then combine them into one graph. Each piece is graphed only over its defined interval, and we use open or closed circles to indicate whether endpoints are included.

Examples

Book overview

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

Continue this chapter

Chapter 4: Writing Linear Functions

  1. Lesson 1

    Lesson 1: Writing Equations in Slope-Intercept Form

    LearnPractice
  2. Lesson 2

    Lesson 2: Writing Equations in Point-Slope Form

    LearnPractice
  3. Lesson 3

    Lesson 3: Writing Equations of Parallel and Perpendicular Lines

    LearnPractice
  4. Lesson 4

    Lesson 4: Scatter Plots and Lines of Fit

    LearnPractice
  5. Lesson 5

    Lesson 5: Analyzing Lines of Fit

    LearnPractice
  6. Lesson 6

    Lesson 6: Arithmetic Sequences

    LearnPractice
  7. Lesson 7Current

    Lesson 7: Piecewise Functions

    LearnPractice