Types of Functions

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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 non-negative value of x.

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What is a Square Root Function?

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A Square Root Function is a function that involves the square root of a variable. It is defined as f(x) = √x, where x is non-negative.

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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) = ax^2 + bx + c, where a, b, and c are constants and a ≠ 0.

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What is a Linear Function?

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A Linear Function is a function that graphs to a straight line. It is defined as f(x) = mx + b, where m is the slope and b is the y-intercept.

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What is an Exponential Function?

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An Exponential Function is a function in which an independent variable is in the exponent. It is typically in the form f(x) = a * b^x, where a is a constant and b is the base.

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What does it mean for a relation to be 'not a function'?

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A relation is 'not a function' if it does not pass the vertical line test, meaning that for at least one input, there are multiple outputs.

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Example of an Absolute Value Function: What is f(x) = 5 + 3|x - 2|?

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This is an Absolute Value Function because it includes the absolute value expression |x - 2|.

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Example of a Square Root Function: What is y = √(2x)?

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This is a Square Root Function because it involves the square root of the variable x.

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Example of a Quadratic Function: What is y = x^2 - 3x + 4?

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This is a Quadratic Function because it is a polynomial of degree 2.

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Example of a Linear Function: What is f(x) = 2x + 1?

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This is a Linear Function because it can be represented as a straight line on a graph.