Functions Review

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

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What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function. If any vertical line intersects the graph at more than one point, it is not a function.

Front

What is the Horizontal Line Test?

Back

The Horizontal Line Test is used to determine if a function is one-to-one. If any horizontal line intersects the graph at more than one point, the function is not one-to-one.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. Its general form is 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. Examples include quadratic functions, exponential functions, and trigonometric functions.

Front

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

Back

A relation is a function if every input is associated with exactly one output.

Front

Can a vertical line intersect a function more than once?

Back

No, if a vertical line intersects a graph more than once, the relation is not a function.

Front

What is an example of a nonlinear equation?

Back

An example of a nonlinear equation is y = x^2.

Front

What is an example of a linear equation?

Back

An example of a linear equation is y = 2x + 3.

Front

What is the definition of a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.