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Difference Quotients

"To find the slope of the secant line between two points in a function, we use difference quotients. Difference quotients are used with limits in the definition of the derivative and are important to ...

Determining Whether a Relation is a Function

"Understanding relations (defined as a set of inputs and corresponding outputs) is an important step to learning what makes a function. A function is a specific relation, and determining whether a rel ...

Derivative Definition

"The definition of the derivative is the slope of a line that lies tangent to the curve at the specific point. The limit of the instantaneous rate of change of the function as the time between measure ...

Definition of Inverse

"The definition of a function can be extended to define the definition of inverse of a function. Along with one to one functions, invertible functions are an important type of function. The definition ...

Defining Variables

"Variables are used throughout math after Algebra, and are important to understand. A defining variable is a symbol, such as x, used to describe any number. When a variable is used in an equation or a ...

Quadratic Graphs

"When we graph quadratic functions, we always get a parabola (or U) shape and symmetry in the table and graph. One easy way to complete quadratic graphs is to make a table of values by plugging in x-v ...

Continuity of a Function

"In order for a function to be continuous at a certain point, three conditions must be met: (1) that the point is in the domain of the function, (2) that the two-sided limit of the function as it appr ...

One to One Function

"After learning the definition of a function, we can extend it to define a one to one function. A one to one function has not only one output for every input, but also only one input in the domain for ...

Average Value of a Function

"Calculating the average value of a function over a interval requires using the definite integral. The exact calculation is the definite integral divided by the width of the interval. This calculates ...

Antiderivatives

"Antiderivatives are the opposite of derivatives. An antiderivative is a function that reverses what the derivative does. One function has many antiderivatives, but they all take the form of a functio ...

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