Classifying 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 quadratic function?

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A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

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What is an exponential function?

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An exponential function is a mathematical function of the form f(x) = a * b^x, where a is a constant, b is the base (a positive real number), and x is the exponent.

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What is a cubic function?

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A cubic function is a polynomial function of degree 3, typically in the form f(x) = ax³ + bx² + cx + d, where a, b, c, and d are constants and a ≠ 0.

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What is an absolute value function?

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An absolute value function is a function that returns the non-negative value of its input, defined as f(x) = |x|. It is V-shaped when graphed.

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How do you identify a linear function from a graph?

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A linear function will produce a straight line when graphed. It has a constant rate of change (slope) and no curves.

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How do you identify a quadratic function from a graph?

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A quadratic function will produce a parabolic shape (U-shaped) when graphed. It can open upwards or downwards depending on the sign of the leading coefficient.

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How do you identify an exponential function from a graph?

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An exponential function will show rapid growth or decay. It will not cross the x-axis and has a characteristic curve that increases or decreases sharply.

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How do you identify a cubic function from a graph?

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A cubic function will produce an S-shaped curve when graphed. It can have one or two turning points and can cross the x-axis up to three times.

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What is the general form of a linear function?

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The general form of a linear function is f(x) = mx + b, where m is the slope and b is the y-intercept.