Characteristics of Linear Functions

This video tutorial introduces linear functions, explaining their characteristics and how to identify them by comparing graphs. It reviews basic concepts of functions, including independent and dependent variables, and how to plot points on a coordinate plane. The tutorial discusses the nature of linear functions as straight lines and clarifies why vertical lines are not considered linear functions. It also introduces nonlinear functions and provides examples to help distinguish between linear and nonlinear functions.

What is the relationship between the input and output in a linear function?

• The output is always half of the input.

• The output is always the square of the input.

• The output is always the input plus one.

• The output is always three times the input.

When plotting points on a coordinate plane, where do you start?

• At any random point

• At the bottom left corner

• At the origin

• At the top right corner

How is an ordered pair written?

• y, x

• x, y

• y - x

• x - y

What do all linear function graphs have in common?

• They are all vertical lines.

• They are all curved lines.

• They are all horizontal lines.

• They are all straight lines.

Why are vertical lines not considered linear functions?

• They do not intersect the x-axis.

• They are not straight lines.

• They have more than one output for a single input.

• They have no slope.

What is a nonlinear function?

• A function that forms a straight line

• A function that forms a horizontal line

• A function that forms a vertical line

• A function that forms a curved line

Which of the following is an example of a nonlinear function?

• y = x^2

• y = 3x

• y = 2x + 1

• y = x - 4

How can you determine if a function is linear by plotting points?

• If the points form a zigzag pattern

• If the points form a circle

• If the points form a square

• If the points form a straight line

What is the significance of the slope in a linear function?

• It determines the color of the line.

• It determines the width of the line.

• It determines the length of the line.

• It determines the direction and steepness of the line.

Which of the following is NOT a characteristic of a linear function?

• It has a constant slope.

• It forms a straight line.

• It can have multiple outputs for a single input.

• It has a consistent rate of change.