Exploring Linear and Non-Linear Functions

The video tutorial explains the difference between linear and non-linear functions. It covers how to identify linear functions through equations, tables, and graphs, emphasizing the importance of a constant rate of change. Examples include quadratic and cubic functions, which are non-linear, and linear functions, which are characterized by a straight line graph. The tutorial concludes with a summary of key concepts and learning objectives.

What is the standard form of a linear equation?

• y = mx + b

• y = x^2 + b

• y = m/x + b

• y = mx^2 + b

What does the 'm' in the linear equation represent?

• Y-intercept

• Slope

• Maximum value

• X-intercept

What does the y-intercept represent in a linear equation?

• The maximum value of the function

• The point where the line crosses the y-axis

• The slope of the line

• The rate of change

How can you tell if a function is linear by looking at a graph?

• It forms a parabola

• It is a straight line

• It zigzags

• It forms a circle

What makes a table represent a linear function?

• Values squared

• Constant rate of change

• Decreasing values

• Random rate of change

What shape does a non-linear function form when graphed?

• Triangle

• Straight line

• Circle

• Parabola

What is a key difference between linear and non-linear equations?

• Linear equations have a visible exponent on x

• Non-linear equations have a constant rate of change

• Non-linear equations always pass through the origin

• Linear equations can be written in the form y = mx + b

What does a constant rate of change in a table indicate?

• Cyclical pattern

• Exponential growth

• Linear function

• Quadratic function

Why is a function with x raised to the power of 3 not linear?

• It is proportional

• It forms a straight line

• It has a constant rate of change

• It does not have a constant rate of change

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

• It forms a u-shaped graph

• It has a constant rate of change

• It can be represented by y = mx + b

• It produces a straight line when graphed