Exploring Linear and Nonlinear Functions

The video tutorial explains the differences between linear and non-linear functions. It covers the characteristics of linear functions, such as a constant change in y with respect to x, and how they are represented in equations, graphs, and tables. Non-linear functions are identified by features like exponents greater than one, multiplication of variables, and variables in denominators. The tutorial provides examples and uses graphing to illustrate these concepts, emphasizing the importance of constant change in determining linearity.

What is a key characteristic of a linear function?

• x and y appear in the denominators.

• x and y are always multiplied together.

• A constant change in x results in a variable change in y.

• A constant change in x results in a constant change in y.

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

• 2/x = y

• x + y = 7

• y = 2^x

• x^2 + 3 = y

What makes a function non-linear?

• x and y are added together.

• x and y have exponents of one.

• x and y are multiplied together.

• x and y appear in the numerator.

How is a linear function represented on a graph?

• As a horizontal line.

• As a curve.

• As a non-vertical straight line.

• As a vertical line.

Which of the following graphs represents a non-linear function?

• A horizontal line.

• A curve.

• A vertical line.

• A straight line.

In a table, what indicates a linear function?

• The change in y is variable for a constant change in x.

• The change in y is constant for a constant change in x.

• The change in x is constant for a variable change in y.

• The change in x and y are both variable.

If the x values in a table increase by 1 and the y values increase by 2, what type of function is it?

• Exponential

• Linear

• Non-linear

• Quadratic

Which of the following equations is non-linear?

• y = x + 7

• y = 2x + 5

• y = x/2 - 1

• y = x^3 + 3

What happens to the y values in a non-linear function table?

• They decrease by a constant amount.

• They increase by a constant amount.

• They remain the same.

• They change by a variable amount.

In the equation y = x/2 - 1, why is it considered linear?

• Because x has an exponent.

• Because x is in the denominator.

• Because x is in the numerator.

• Because x is under a square root.