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 f(x) = 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 a Nonlinear Function?

Back

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

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 there are at least two ordered pairs with the same first element but different second elements, meaning one input does not have a unique output.

Tags

CCSS.8.F.A.1

Front

Example of a Linear Function: f(x) = 2x + 3. What is the slope?

Back

The slope (m) is 2.

Tags

CCSS.8.EE.B.5

Front

Example of a Nonlinear Function: f(x) = x^2. What is the shape of its graph?

Back

The graph of f(x) = x^2 is a parabola.

Tags

CCSS.HSF-IF.C.7A

Front

What is the y-intercept in the function f(x) = -3x + 5?

Back

The y-intercept is 5.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

Identify if the following is a function: {(1, 2), (1, 3), (2, 4)}.

Back

This relation is not a function because the input 1 has two different outputs (2 and 3).

Tags

CCSS.8.F.A.1

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 is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has exactly one output, while a relation can have multiple outputs for a single input.

Tags

CCSS.8.F.A.1

Front

Graph the function f(x) = 3x - 1. What is the y-intercept?

Back

The y-intercept is -1.

Tags

CCSS.HSF-IF.C.7A