Linear vs Nonlinear functions

Front

What is a function in mathematics?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Tags

CCSS.8.F.A.1

Front

How can you determine if a graph represents a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line, characterized by a constant rate of change and can be expressed in the form y = mx + b.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, meaning the rate of change is not constant.

Tags

CCSS.8.F.A.3

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What are some examples of nonlinear functions?

Back

Examples of nonlinear functions include quadratic functions (y = ax^2 + bx + c), exponential functions (y = a * b^x), and trigonometric functions (y = sin(x), y = cos(x)).

Front

What is the slope of a linear function?

Back

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

Tags

CCSS.8.EE.B.5

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if its output values fall as the input values increase.

Front

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

Back

A linear function will have a constant difference in the output values for equal intervals of input values.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.

Tags

CCSS.HSF-IF.C.7A