All quadratic functions fit the form y = Ax 2 + Bx + C, where A, B, and C can be any real number (although A cannot be zero). The function y = x 2 is the most basic quadratic function.
Quadratic Function: A quadratic function is a function in which the independent variable is squared. The decay of nuclear waste is an example of exponential decay. The function y = (.5)x is an exponential decay function as x increases, y decreases. Population growth and investment growing with interest are examples of exponential growth.Įxponential Decay Function: An exponential decay function is an exponential function that decreases. The function y = 3 x is an exponential growth function as x increases, y increases. For example, in y = 2 x, each time x grows by 1, y is multiplied by 2.īase: In the exponential equation 8 = 2 3, 2 is the base and 3 is the exponent.Įxponent: In the exponential equation 8 = 2 3, 2 is the base and 3 is the exponent.Įxponential Growth Function: An exponential growth function is an exponential function that increases. An exponential function has a constant ratio between successive outputs. Functions like y = 2 x and y = 10(.5) x are exponential functions. In a table with inputs and outputs, the input is the independent variable and the output is the dependent variable.Įxponential Function: In an exponential function the independent variable is an exponent in an equation. In a table with inputs and outputs, the input is the independent variable and the output is the dependent variable.ĭependent Variable: In a function where the value of variable A depends on the value of variable B, variable A is referred to as the dependent variable and variable B is referred to as the independent variable. Independent Variable: In a function where the value of variable A depends on the value of variable B, variable A is referred to as the dependent variable and variable B is referred to as the independent variable. It is possible for a function to have more than one input that yields the same output. For example, a recursive description might be, “Add two to the value of the output each time the input goes up by one.” The Fibonacci sequence, where each output is the sum of the two numbers before it, is a recursive description of a pattern.įunction: A function is any relationship between inputs and outputs in which each input leads to exactly one output.
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Recursive Description: A recursive description of a pattern tells you how to proceed from one step to the next. A rule such as “take the input, triple it, and add two” is a closed-form description of a pattern. Closed-Form Description: A closed-form description of a pattern tells how to get from any input to its output, without having to know any previous outputs.
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