Linear and Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed. Its graph can be a curve or any other shape that is not linear.

Front

Identify the linear function from the following: y = 2x + 4, y = 2x² + 4, y = 2x(4 - 3x), xy = 15.

Back

y = 2x + 4

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one y-value.

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if it passes the vertical line test, meaning that no vertical line intersects the graph at more than one point.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a graph of a function. If a vertical line crosses the graph at more than one point, it is not a function.

Front

Which of the following ordered pairs would prevent a table from being a function? (10, 10), (2, 4), (6, 1), (-2, 0)

Back

(-2, 0) - because it would create a duplicate x-value.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, represented by 'm' in the equation y = mx + b. It indicates how much y changes for a unit change in x.

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by 'b' in the equation y = mx + b.

Front

Identify the linear functions from the following: Function I: y = 3x + 1, Function II: y = x² - 2, Function III: y = -4x + 5.

Back

Function I and Function III are linear.