Exploring Linear Relationships in Expressions

The video tutorial explains linear and nonlinear functions, focusing on their characteristics, how to identify them using tables and graphs, and the properties of linear and nonlinear equations. Linear functions are defined by a constant rate of change and graph as a straight line, while nonlinear functions have variable rates and curved graphs. The tutorial also covers how to determine linearity through graphing and analyzing equations.

What is a key characteristic of a linear function?

• It forms a curved line.

• It has multiple outputs for one input.

• It can be a vertical line.

• It has a constant rate of change.

Which of the following is true about nonlinear functions?

• They can be vertical lines.

• Their rate of change is not constant.

• They form straight lines.

• They have a constant rate of change.

How can you determine if a table represents a linear function?

• By checking if the rate of change for both x and y is constant.

• By ensuring all x values are the same.

• By ensuring all y values are the same.

• By checking if the table has more than 5 rows.

In a linear function table, if x increases by 1 and y decreases by 15 consistently, is it a linear function?

• Yes, because x is increasing.

• No, because y is decreasing.

• No, because the rate of change is not constant.

• Yes, because the rate of change is constant.

What does it mean if the points plotted from a table form a straight line?

• The function has no rate of change.

• The function is undefined.

• The function is nonlinear.

• The function is linear.

Which of the following equations represents a linear function?

• y = 2x + 3

• y = 3xy

• y = 4/x

• y = x^2 + 1

Why is the equation y = 1 - x^2 not a linear function?

• Because it forms a straight line.

• Because it has a constant rate of change.

• Because it has an exponent.

• Because it has a variable in the denominator.

What is the graphical representation of the equation y = 4.7?

• A vertical line

• A diagonal line

• A curved line

• A horizontal line

If a table shows x values increasing by 1 and y values increasing by 3, what type of function is it?

• Nonlinear

• Undefined

• Linear

• Exponential

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

• Forms a straight line when graphed

• Has a constant rate of change

• Cannot be a vertical line

• Can have an exponent in the equation