Evaluating Piecewise Functions: Key Concepts

The video tutorial introduces piecewise functions, outlining the lesson's objectives to evaluate and graph these functions. It defines piecewise functions as those with different expressions over various intervals, contrasting them with standard functions. The tutorial provides examples and practice problems to illustrate how to evaluate piecewise functions based on given conditions, ensuring students understand the process of selecting the correct expression for different input values.

What is the main objective of the lesson?

• To solve quadratic equations

• To understand linear functions

• To evaluate and graph piecewise functions

• To learn about trigonometric functions

How are piecewise functions defined?

• As functions with a single algebraic expression

• As functions that only use linear expressions

• As functions that are always continuous

• As functions that are defined differently over different intervals

Which of the following is an example of a non-piecewise function?

• f(x) = 2x - 4 if x > 0

• f(x) = 5x + 3 if x >= -2

• f(x) = x^2 + 1

• f(x) = x^2 - 1 if x < -2

What is the value of f(-5) for the given piecewise function?

• 22

• 23

• 25

• 24

Which condition does x = -5 satisfy in the piecewise function?

• x = -2

• x >= -2

• x < -2

• x > -2

What is the value of f(-2) for the given piecewise function?

• 7

• -7

• 5

• -5

Which condition does x = -2 satisfy in the piecewise function?

• x >= -2

• x > -2

• x = -2

• x < -2

What is the value of f(7) for the given piecewise function?

• 35

• 38

• 42

• 40

Which condition does x = 7 satisfy in the piecewise function?

• x < -2

• x = -2

• x > -2

• x >= -2

What is the value of f(0) for the given piecewise function?

• 3

• 5

• 8

• 7