Comparing Linear and Non-Linear Functions

Mr. Buffington introduces graphs of functions, focusing on linear and nonlinear types. Linear functions have a constant rate of change, represented by a slope, and can be expressed in forms like slope-intercept. Nonlinear functions, such as quadratic and cubic, have variables raised to powers greater than one, resulting in curves or waves. The video explains the difference between functions and relations using the vertical line test. Examples of nonlinear functions include parabolas and sine waves. The lesson concludes with sample questions to distinguish between linear and nonlinear functions.

What is the main difference between linear and nonlinear functions?

• Linear functions have variables raised to the power of 2 or more.

• Nonlinear functions form straight lines.

• Linear functions have variables raised to the power of 1.

• Nonlinear functions can be written in slope-intercept form.

Which form is most useful for linear functions?

• Standard form

• Slope-intercept form

• Point-slope form

• Quadratic form

What is the characteristic of a linear function's graph?

• It forms a wave.

• It forms a parabolic curve.

• It forms a straight line.

• It forms a circle.

What happens when the variable in a function is raised to the power of 2?

• It forms a straight line.

• It forms a parabolic curve.

• It forms a wave.

• It forms a circle.

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

• y = x^2

• y = 2x - 5

• y = 3x + 2

• y = 4x + 1

What type of graph does the function y = x^3 form?

• A circle

• A squiggly line

• A parabolic curve

• A straight line

What is a common real-world example of a nonlinear function?

• Comparing the side length of a square to its area

• Counting the number of cans in a pack

• Calculating the distance traveled at a constant speed

• Converting yards to feet

What is the key factor in identifying a linear function in a word problem?

• A constant rate of change or slope

• The presence of a variable raised to the power of 2

• The function forming a parabolic curve

• The function forming a wave

Which of the following describes a linear relationship?

• The area of a square with side length x

• The graph of y = x^2

• The number of feet in x yards

• The volume of a cube with side length x

What is the slope in the equation y = 3x + 2?

• 2

• 3

• x

• y