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.

Front

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.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise/run).

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

Back

A relation is a function if every input (x-value) has exactly one output (y-value). This means no x-value can be paired with more than one y-value.

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What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point in a coordinate system, written in the form (x, y).

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How can you determine if a table represents a function?

Back

A table represents a function if each x-value corresponds to only one y-value. If any x-value is repeated with different y-values, it is not a function.

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What is the y-intercept of a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis. It occurs when x = 0.

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

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph is curved, indicating a variable rate of change.

Front

What is a quadratic function?

Back

A quadratic function is a type of nonlinear function that can be expressed in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.

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What is a function table?

Back

A function table is a table that displays pairs of input (x) and output (y) values for a function, showing how each input relates to its output.