Example Function A ... AWS
Key Terms Function
Definition A mathematical relation in which each input (xvalue) is related to exactly one output (y-value). The set of all possible x-values for a given function is called the domain; the set of all possible y-values for a given function is called the range. (See below) Functions can be represented by equations (such as ( ) √ ), tables (such as T-tables), and graphs (such as the squiggly graph at the right).
Domain
The set of all possible x-values in a given function; the set from which the input numbers come. Some types of functions have a restricted domain, meaning that not every number can be a possible value for x. Example: for the function ( ) √ , we can see that x must be greater than 0, since we can’t take the square root of a negative number.
Range
The set of all possible y-values that are generated by a given function; the set of output numbers. Some types of functions have a restricted range, meaning that not every number is a value for y that can be generated by the function. Example: for the function ( ) we can see that the y-values can never be negative, because when x is squared the output will always be positive (or zero).
Illustration/Example This function takes an input number, x, and adds 5 to it. ( ) This function takes an input number, x, and squares it. X -3 -2 -1 0 1 2
Y 2 1 0 -1 -2 -3
Relation
A set of ordered pairs of numbers.
X -3 -2 -1 0 1 2 {
T-table
A table organizing the input (domain; x-values) and output (range; y-values). The table is generated given an equation. We get to choose x-values, and then we solve for the y-values.
Graph
Set of data represented by points on a coordinate plane.
{
X -3 -1 0 1 Lines
Linear functions produce lines. Quadratic Functions produce parabolas. Graphs of various kinds of functions have unique shapes.
Trigonometric functions
Y 2 1 0 -1 -2 -3 } Y 2 0 -1 -2 Parabolas
}
Point
The position ( ) of a place on the coordinate plane, represented with a “dot” on the graph. Points on the line make the equation true when plugged in algebraically.
( Vertical Line Test
A test used to determine if a relation is a function. When given a graph, dray a vertical line; if the graph intersects the line more than once, it is not a function (see illustration).
X-Value
Independent variable; the first value in an ordered ) pair ( Dependent variable; the second value in an ordered ) pair ( Input values (x-values; domain) that are chosen to calculate the output values (y-values).
Y-Value Independent Variable
Dependent Variable
The x-value is referred to as the “independent” variable because it is the INPUT number – its value is not determined by the function, but rather, we get to choose it. Output values (y-values; range) that are the result of the input values (x-values).
)
(
) are points on the line.
( ); x-value: -2 ( ); x-value: 5 ( ); y-value: 5 ( ); y-value: 0 X-values in a table, on a graph, in a set of ordered pairs
Y-values in a table, on a graph, in a set of ordered pairs
Definition A mathematical relation in which each input (xvalue) is related to exactly one output (y-value). The set of all possible x-values for a given function is called the domain; the set of all possible y-values for a given function is called the range. (See below) Functions can be represented by equations (such as ( ) √ ), tables (such as T-tables), and graphs (such as the squiggly graph at the right).
Domain
The set of all possible x-values in a given function; the set from which the input numbers come. Some types of functions have a restricted domain, meaning that not every number can be a possible value for x. Example: for the function ( ) √ , we can see that x must be greater than 0, since we can’t take the square root of a negative number.
Range
The set of all possible y-values that are generated by a given function; the set of output numbers. Some types of functions have a restricted range, meaning that not every number is a value for y that can be generated by the function. Example: for the function ( ) we can see that the y-values can never be negative, because when x is squared the output will always be positive (or zero).
Illustration/Example This function takes an input number, x, and adds 5 to it. ( ) This function takes an input number, x, and squares it. X -3 -2 -1 0 1 2
Y 2 1 0 -1 -2 -3
Relation
A set of ordered pairs of numbers.
X -3 -2 -1 0 1 2 {
T-table
A table organizing the input (domain; x-values) and output (range; y-values). The table is generated given an equation. We get to choose x-values, and then we solve for the y-values.
Graph
Set of data represented by points on a coordinate plane.
{
X -3 -1 0 1 Lines
Linear functions produce lines. Quadratic Functions produce parabolas. Graphs of various kinds of functions have unique shapes.
Trigonometric functions
Y 2 1 0 -1 -2 -3 } Y 2 0 -1 -2 Parabolas
}
Point
The position ( ) of a place on the coordinate plane, represented with a “dot” on the graph. Points on the line make the equation true when plugged in algebraically.
( Vertical Line Test
A test used to determine if a relation is a function. When given a graph, dray a vertical line; if the graph intersects the line more than once, it is not a function (see illustration).
X-Value
Independent variable; the first value in an ordered ) pair ( Dependent variable; the second value in an ordered ) pair ( Input values (x-values; domain) that are chosen to calculate the output values (y-values).
Y-Value Independent Variable
Dependent Variable
The x-value is referred to as the “independent” variable because it is the INPUT number – its value is not determined by the function, but rather, we get to choose it. Output values (y-values; range) that are the result of the input values (x-values).
)
(
) are points on the line.
( ); x-value: -2 ( ); x-value: 5 ( ); y-value: 5 ( ); y-value: 0 X-values in a table, on a graph, in a set of ordered pairs
Y-values in a table, on a graph, in a set of ordered pairs
