Understanding Linear Functions and Domains

The video tutorial explains how to read graphs and write piecewise functions. It covers the analysis of three linear functions, focusing on finding slopes, y-intercepts, and domains. The tutorial also includes a word problem about a cell phone plan, demonstrating how to apply piecewise functions to calculate costs based on usage. The video emphasizes understanding domains and inequalities in piecewise functions.

What is the primary focus of piecewise functions?

• To determine the area under a curve

• To calculate integrals

• To analyze and write functions from graphs

• To solve quadratic equations

How do you determine the slope of a linear function from a graph?

• By counting the rise over run

• By finding the y-intercept

• By calculating the area under the line

• By measuring the angle with the x-axis

What is the y-intercept of the first function discussed?

• 0

• 4

• -4

• 2

For the first function, what is the domain?

• x > -2

• x ≥ -2

• x < -2

• x ≤ -2

What characterizes a flat line in a graph?

• It is a constant y-value

• It is parallel to the y-axis

• It has a negative slope

• It has a positive slope

What is the domain for the second function?

• -2 ≤ x < 3

• -2 < x < 3

• -2 < x ≤ 3

• -2 ≤ x ≤ 3

How is the slope of the third function described?

• Positive and increasing

• Undefined

• Zero and constant

• Negative and decreasing

What is the domain for the third function?

• 3 < x < 6

• 3 ≤ x < 6

• 3 ≤ x ≤ 6

• 3 < x ≤ 6

What is the initial cost of the cell phone plan?

• $15

• $35

• $50

• $20

How much is charged per minute after 500 minutes?

• 10 cents

• 20 cents

• 25 cents

• 15 cents