Linear and 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 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 shape that is not linear, such as quadratic or exponential functions.

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What does it mean for a relation to be 'Not a Function'?

Back

A relation is 'not a function' if there are at least two ordered pairs with the same first element but different second elements. This violates the definition of a function, which states that each input must have exactly one output.

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Give an example of a Linear Function.

Back

An example of a linear function is f(x) = 2x + 3. This function has a constant rate of change and its graph is a straight line.

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Give an example of a Nonlinear Function.

Back

An example of a nonlinear function is f(x) = x^2. This function forms a parabola when graphed, which is not a straight line.

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What is the slope in a linear function?

Back

The slope (m) in a linear function represents the rate of change of the function. It indicates how much the output (y) changes for a unit change in the input (x).

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What is the y-intercept in a linear function?

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The y-intercept (b) in a linear function is the point where the graph intersects the y-axis. It represents the value of the function when x = 0.

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How can you identify a Nonlinear Function from its graph?

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A nonlinear function can be identified from its graph by looking for curves or shapes that are not straight lines. If the graph changes direction, it is nonlinear.

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What is the difference between a function and a relation?

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A function is a specific type of relation where each input is associated with exactly one output. A relation can have multiple outputs for a single input.

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What is a quadratic function?

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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 and a ≠ 0.