Functions and Linear Functions Review

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.

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What is a nonlinear function?

Back

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

Front

How can you determine if a graph represents a function?

Back

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

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What is the slope of a line?

Back

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

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What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of a function crosses the y-axis, represented as (0, b) in the function f(x) = mx + b.

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

Back

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

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, while a nonlinear graph can be curved or take on various shapes.

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What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

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What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2 (a quadratic function).

Front

What is the equation of a line in slope-intercept form?

Back

The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.