Types of Functions

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What is a function?

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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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What is a linear function?

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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 an absolute value function?

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An absolute value function is a function that contains an absolute value expression. It is defined as f(x) = |x|, which outputs the distance of x from 0 on the number line.

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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.

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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, and x is the exponent.

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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.

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How do you identify an absolute value function from its equation?

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An absolute value function can be identified by the presence of the absolute value symbol | | in its equation, such as f(x) = |x - 3|.

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What is the graph of a quadratic function like?

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The graph of a quadratic function is a parabola, which opens upwards if the coefficient of x² is positive and downwards if it is negative.

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What is the key characteristic of an exponential function?

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The key characteristic of an exponential function is that it grows (or decays) at a rate proportional to its current value.

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What does the slope of a linear function represent?

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The slope of a linear function represents the rate of change of the function; it indicates how much y changes for a unit change in x.