Exploring Linear and Nonlinear Functions

What is the basic equation form of a linear function?

• y = ax^2 + bx + c

• y = log(x)

• y = mx + b

• y = a/x

Which of the following is true about a linear function?

• Its graph is a curve.

• It has a variable rate of change.

• It has a constant rate of change.

• It has multiple outputs for a single input.

What is a key characteristic of a nonlinear function?

• It has a constant rate of change.

• Its graph is a straight line.

• It does not increase or decrease at a constant rate.

• It follows the equation y = mx + b.

In a table, what indicates that a function is linear?

• There is a constant rate of change between input and output values.

• The output values are random.

• The input values are random.

• The input values decrease while the output values increase.

If the input increases by 7 and the output increases by 5, what is the slope?

• 2/1

• 1/2

• 7/5

• 5/7

What does a straight line on a graph indicate about the function?

• It is nonlinear.

• It has a variable rate of change.

• It is linear.

• It has no relation between input and output.

Which of the following graphs represents a nonlinear function?

• A straight line

• A vertical line

• A curve

• A horizontal line

What is the slope if the x-values increase by 2 and the y-values decrease by 4?

• 4

• -4

• -2

• 2

Why is a function with two separate linear sections considered nonlinear?

• Because it has a constant rate of change.

• Because it can be graphed with one straight line.

• Because it does not form a single straight line.

• Because it has multiple outputs for a single input.

What is a key difference between linear and nonlinear functions?

• Nonlinear functions follow the equation y = mx + b.

• Linear functions have a variable rate of change.

• Nonlinear functions have a constant rate of change.

• Linear functions form a straight line on a graph.