Lesson 3-2 Independent Check: Linear and Nonlinear Functions

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph. It has a constant rate of change and can be expressed in 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. It has a variable rate of change and can include curves, parabolas, and other shapes.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This means no x-value can be paired with more than one y-value.

Front

How can you determine if a table represents a function?

Back

A table represents a function if each x-value is unique. If any x-value is repeated with different y-values, it is not a function.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run). It indicates the steepness and direction of the line.

Front

What is the y-intercept of a linear function?

Back

The y-intercept of a linear function is the point where the line crosses the y-axis. It is the value of y when x is 0.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point on a graph, written in the form (x, y), where x is the horizontal coordinate and y is the vertical coordinate.

Front

What is the difference between a linear function and a nonlinear function in terms of graph shape?

Back

A linear function graphs as a straight line, while a nonlinear function graphs as a curve or other non-straight shape.

Front

What is a table of values in relation to functions?

Back

A table of values lists pairs of x and y values that represent a function. It helps visualize the relationship between the input and output.

Front

How can you identify a nonlinear function from a table?

Back

You can identify a nonlinear function from a table if the change in y-values is not consistent for equal changes in x-values.