Linear and Nonlinear Functions

Front

What is a function?

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

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves or other shapes.

Tags

CCSS.8.F.A.3

Front

What does the vertical line test determine?

Back

The vertical line test determines if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which graphs as a straight line.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which graphs as a parabola.

Tags

CCSS.8.F.A.3

Front

What does it mean for a relation to be 'not a function'?

Back

A relation is 'not a function' if at least one input is associated with more than one output.

Tags

CCSS.8.F.A.1

Front

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

Back

To identify a function from a table, check if each input (x-value) corresponds to exactly one output (y-value). If any input has multiple outputs, it is not a function.

Tags

CCSS.8.F.A.1

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Tags

CCSS.8.EE.B.5

Front

What is a y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented by the value of y when x = 0.