3.2 Linear 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.

Front

Which of the following sets of values is a function? (9,5) (10,5) (9,-5) (10,-5), (3,4) (4,-3) (7,4) (3, 8), (6,-5) (7, -3) (8, -1) (9, 1), (2, -2) (5, 9) (5, -7) (1, 4)

Back

(6,-5) (7, -3) (8, -1) (9, 1) is a function because each first element (x-value) is unique.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented in the Cartesian plane as a straight line.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, meaning it can have curves or bends.

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

Is the equation y = 2x + 3 linear or nonlinear?

Back

Linear.

Front

Is the equation y = x^2 + 2 linear or nonlinear?

Back

Nonlinear.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, typically representing a relationship between two sets.

Front

Is the relation {(1,2), (2,3), (3,4)} a function?

Back

Yes, because each input (first element) is associated with exactly one output (second element).

Front

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

Back

For a relation to be a function, each input must correspond to exactly one output.