Linear Functions and Their Properties

The video tutorial explains how to identify key characteristics of linear functions, including finding x and y intercepts, determining if a line is increasing or decreasing, and understanding the domain and range. The tutorial provides step-by-step instructions and examples to help learners grasp these concepts effectively.

What are the first two characteristics of a linear function discussed in the video?

• Slope and curvature

• X and Y intercepts

• Domain and range

• Increasing and decreasing nature

How do you determine the x-intercept of a linear function?

• By calculating the slope

• By finding where the line crosses the x-axis

• By checking the domain

• By finding where the line crosses the y-axis

What is the ordered pair for the x-intercept in the example given?

• (0, 3)

• (-2, 0)

• (0, -2)

• (3, 0)

How can you tell if a line is increasing?

• The slope is positive, going up from left to right

• The line is horizontal

• The line goes down from left to right

• The slope is zero

What does a negative slope indicate about a line?

• The line is increasing

• The line is horizontal

• The line is decreasing

• The line is vertical

What is the domain of a linear function with arrows on both ends?

• All real numbers

• All negative numbers

• Only integers

• All positive numbers

How is the range of a linear function with arrows on both ends described?

• All negative numbers

• All positive numbers

• All real numbers

• Only integers

In inequality notation, how is the domain of a linear function with arrows on both ends expressed?

• x < 0

• x > 0

• -∞ < x < ∞

• 0 < x < 1

What does the presence of arrows on both ends of a line indicate about its domain and range?

• They are limited to integers

• They include all real numbers

• They are limited to negative numbers

• They are limited to positive numbers

What symbol is used to represent all real numbers?

• A fancy R

• A fancy Z

• A fancy Q

• A fancy N