Linear/NonLinear Functions

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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 y = 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 rate of change is not constant, and it can take various forms such as quadratic, exponential, or logarithmic.

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How can you identify a linear graph?

Back

A linear graph can be identified by its straight line, which indicates a constant rate of change between the variables.

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What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise/run).

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What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the value of y when x is 0.

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What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

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What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

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What is an example of a nonlinear function?

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An example of a nonlinear function is y = x^2, which represents a parabola.

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What is the difference between discrete and continuous functions?

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Discrete functions have distinct, separate values (like points on a graph), while continuous functions have an unbroken line or curve.

Front

How do you determine if a relationship is linear or nonlinear from a table of values?

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If the differences between consecutive y-values are constant for equal intervals of x, the relationship is linear; otherwise, it is nonlinear.