Linear vs Nonlinear functions

Front

What is a function in mathematics?

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.

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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).

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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, characterized by a constant rate of change and can be expressed in the form y = mx + b.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not form a straight line when graphed, meaning the rate of change is not constant.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

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What are some examples of nonlinear functions?

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Examples of nonlinear functions include quadratic functions (y = ax^2 + bx + c), exponential functions (y = a * b^x), and trigonometric functions (y = sin(x), y = cos(x)).

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What is the slope of a linear function?

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The slope of a linear function is the ratio of the rise (change in y) to the run (change in x), indicating the steepness and direction of the line.

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What does it mean for a function to be increasing or decreasing?

Back

A function is increasing if its output values rise as the input values increase, and decreasing if its output values fall as the input values increase.

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How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference in the output values for equal intervals of input values.

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What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input is zero.