Determining Linear and Nonlinear Functions

The video tutorial focuses on distinguishing between linear and nonlinear functions. It covers the characteristics of each type, including their equations, graphs, and rates of change. The tutorial provides examples and practice problems to help students identify these functions from tables, graphs, and equations. Key concepts such as slope, constant rate of change, and the form of equations are discussed to aid in understanding.

What is the main question students should focus on during the lesson?

• How to solve equations quickly?

• What strategy can be used to determine if a function is linear?

• How to graph a quadratic function?

• What is the value of pi?

Which of the following is a characteristic of a linear function?

• It has an exponent greater than 1.

• It can be written in the form y = mx + b.

• It has a variable rate of change.

• Its graph is a curve.

What indicates that a function is nonlinear?

• The rate of change is constant.

• The variable x has an exponent other than 1.

• The equation is in the form y = mx + b.

• The graph is a straight line.

In a table, if x increases by 3 and y decreases by 8 consistently, what type of function does it represent?

• Cubic function

• Linear function

• Quadratic function

• Nonlinear function

What does a curve in a graph indicate about the function?

• The function is quadratic.

• The function is linear.

• The function is nonlinear.

• The function is exponential.

If a table shows x increasing by 2 and y increasing by varying amounts, what type of function is it?

• Linear function

• Exponential function

• Nonlinear function

• Logarithmic function

Which equation form indicates a linear function?

• y = |x| + 2

• y = 5x + 7

• y = 4/x

• y = 2x^2 + 3

What makes an equation nonlinear?

• The equation is y = mx + b.

• The graph is a straight line.

• The rate of change is constant.

• The variable x is in the denominator.

Which of the following is a nonlinear function?

• y = 1/x

• y = 7

• y = 5x

• y = 3x + 2

What is the slope of the linear function y = 5/7x?

• 5

• 7

• 5/7

• 0