Linear vs. Nonlinear Functions

The video tutorial explains how to identify linear and nonlinear functions using graphs, tables, and equations. It covers the characteristics of linear functions, such as having a constant rate of change and being represented by the equation y = mx + b. Nonlinear functions, on the other hand, do not have a constant rate of change and include curves or breaks in graphs. The tutorial provides examples and practice problems to help learners distinguish between linear and nonlinear functions.

What is the slope-intercept form of a linear equation?

• y = a^x

• y = ax^2 + bx + c

• y = x^2 + bx + c

• y = mx + b

Which of the following indicates a nonlinear function when analyzing a graph?

• A straight line

• A curve

• A horizontal line

• A vertical line

If a graph has a constant rate of change, what type of function does it represent?

• Nonlinear

• Quadratic

• Linear

• Exponential

In a table, if the change in x and y is constant, what type of function is represented?

• Nonlinear

• Exponential

• Linear

• Quadratic

What does a varying rate of change in a table indicate about the function?

• The function is nonlinear

• The function is exponential

• The function is linear

• The function is quadratic

Which form must an equation be in to confirm it is a linear function?

• y = mx + b

• y = ax^2 + bx + c

• y = a^x

• y = x^3 + bx + c

What does an exponent other than 1 on x in an equation suggest?

• The function is constant

• The function is exponential

• The function is nonlinear

• The function is linear

What type of function is represented by the equation y = 4x + 3?

• Exponential

• Linear

• Quadratic

• Nonlinear

If x is the exponent in an equation, what type of function is it?

• Constant

• Exponential

• Quadratic

• Linear

What shape does a quadratic function form on a graph?

• A hyperbola

• A parabola

• A circle

• A line