For example, the modulus of -1 -1 is 1. The modulus of x, x , is x for values of x which are positive and -x for values of x which are negative. Skip to main content. Search form. Sign up Log in. Functions This section looks at functions within the wider topic of Algebra. The phrase "y is a function of x" means that the value of y depends upon the value of x, so: y can be written in terms of x e. Composing Functions fg means carry out function g, then function f.
This video explains more about the inverse of a function Graphs Functions can be graphed. Algebra 2 How to solve system of linear equations Overview Solving systems of equations in two variables Solving systems of equations in three variables.
Algebra 2 Matrices Overview Basic information about matrices How to operate with matrices Determinants Using matrices when solving system of equations. Algebra 2 Polynomials and radical expressions Overview Simplify expressions Polynomials Factoring polynomials Solving radical equations Complex numbers. Algebra 2 Quadratic functions and inequalities Overview How to graph quadratic functions How to solve quadratic equations The Quadratic formula Standard deviation and normal distribution.
Algebra 2 Conic Sections Overview Distance between two points and the midpoint Equations of conic sections. Algebra 2 Polynomial functions Overview Basic knowledge of polynomial functions Remainder and factor theorems Roots and zeros Descartes' rule of sign Composition of functions. Algebra 2 Rational expressions Overview Variation Operate on rational expressions. Algebra 2 Exponential and logarithmic functions Overview Exponential functions Logarithm and logarithm functions Logarithm property.
If both the input and output are real numbers then the ordered pair can be viewed as the Cartesian coordinates of a point on the graph of the function. Functions are often described as a machine in a box that is open on two ends. You put something into one end of the box, it gets changed inside of the box, and then the result pops out the other end. If you put in a banana you would get back half a banana. If you put in an apple you would get back half an apple. Fruit Halving Function: This shows a function that takes a fruit as input and releases half the fruit as output.
That is, the function divides the input by two. The function machine allows us to alter expressions. In this example, the function would be written as:. Functions can also be thought of as a subset of relations. A relation is a connection between values in one set and values in another. In other words, each number you put in is associated with each number you get out. In a function every input number is associated with exactly one output number In a relation an input number may be associated with multiple or no output numbers.
This is an important fact about functions that cannot be stressed enough: every possible input to the function must have one and only one output.
All functions are relations, but not all relations are functions. Graphs provide a visual representation of functions, showing the relationship between the input values and output values.
Functions have an independent variable and a dependent variable. We say the result is assigned to the dependent variable since it depends on what value we placed into the function. Extend them in either direction past the points to infinity, and we have our graph. Only two points are required to graph a linear function. Let us choose:. Next place these points on the graph, and connect them as best as possible with a curve.
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