Identifying Linear vs Nonlinear Functions

This video tutorial explains how to determine if a function is linear or nonlinear. It covers the characteristics of linear functions, such as having a constant rate of change and being represented by a straight line on a graph. The tutorial also discusses nonlinear functions, which have varying rates of change and may include exponents over variables, resulting in curves or other shapes on a graph. Examples and equations are provided to illustrate these concepts.

What is the first step in determining if a function is linear or nonlinear?

• Check if the function is a relation.

• Establish that the relation is a function.

• Graph the function.

• Calculate the slope.

How can you identify a linear function using a table of values?

• By ensuring the output values are all negative.

• By checking if the input values are all positive.

• By checking if the input values are all even numbers.

• By confirming a constant rate of change in both input and output values.

What form must an equation be in to automatically identify it as linear?

• Quadratic form

• Slope-intercept form

• Exponential form

• Logarithmic form

What is a key characteristic of a nonlinear function?

• It is always in standard form.

• It has a constant rate of change.

• It can be represented by a straight line on a graph.

• It has an exponent over the variable.

How does an exponent over the variable affect the function?

• It makes the function linear.

• It changes the function to nonlinear.

• It has no effect on the function's linearity.

• It makes the function undefined.

What happens to the graph of a nonlinear function?

• It forms a triangle.

• It becomes a circle.

• It forms a straight line.

• It shows a curve or squiggly line.

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

• y = x^2 + 1

• y = 3x - 5

• y = 4x

• y = 2x + 3

What indicates a nonlinear function when looking at a graph?

• The graph is a straight line.

• The graph is a horizontal line.

• The graph is a vertical line.

• The graph has a curve or is not straight.

What is the effect of having an absolute value around the variable in a function?

• It makes the function linear.

• It makes the function nonlinear.

• It has no effect on the function.

• It makes the function undefined.

Which of the following is true about a function with a variable in the denominator?

• It is undefined.

• It is always linear.

• It is always nonlinear.

• It is always quadratic.