In mathematics, an ordered pair (a, b) is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (a, b) is different from the ordered pair (b, a) unless a = b. (In contrast, the unordered pair {a, b} equals the unordered pair {b, a}.)

An ordered pair is a composition of the x coordinate (abscissa) and the y coordinate (ordinate), having two values written in a fixed order within parentheses. It helps to locate a point on the Cartesian plane for better visual comprehension. The numeric values in an ordered pair can be integers or fractions.

Example 1: The Order in Ordered Pairs The first number of an ordered pair is called the first coordinate . The second number of an ordered pair is called the second coordinate .

Ordered pairs are often used to represent two variables. When we write (x, y) = (7, – 2), we mean x = 7 and y = – 2. The number which corresponds to the value of x is called the x-coordinate and the number which corresponds to the value of y is called the y-coordinate.

To figure out if an ordered pair is a solution to an equation, you could perform a test. Identify the x-value in the ordered pair and plug it into the equation. When you simplify, if the y-value you get is the same as the y-value in the ordered pair, then that ordered pair is indeed a solution to the equation.

Is there an ordered pair that is a solution to the linear equations describing BOTH of these lines? Yes. The ordered pair $$ −4,1 is on both lines.

To see if an ordered pair is a solution to an inequality, plug it into the inequality and simplify. If you get a true statement, then the ordered pair is a solution to the inequality. If you get a false statement, then the ordered pair is not a solution.

The solution to a system of linear equations is the ordered pair (or pairs) that satisfies all equations in the system. The solution is the ordered pair(s) common to all lines in the system when the lines are graphed. Lines that cross at a point (or points) are defined as a consistent system of equations.

How do you figure out if a relation is a function? You could set up the relation as a table of ordered pairs. Then, test to see if each element in the domain is matched with exactly one element in the range. If so, you have a function!

Inspect the graph to see if any vertical line drawn would intersect the curve more than once. If there is any such line, the graph does not represent a function. If no vertical line can intersect the curve more than once, the graph does represent a function.

Set B is a function using the rule. Hence, Set C does NOT represent a function. C1(−2,1),C3(−2,−6) have the same x-coordinate value.

The first set of ordered pairs is a function, because no two ordered pairs have the same first coordinates with different second coordinates.

If all possible vertical lines will only cross the relation in one place, then the relation is a function. This works because if a vertical line crosses a relation in more than one place it means that there must be two y values corresponding to one x value in that relation.

Another way to identify the domain and range of functions is by using graphs. Because the domain refers to the set of possible input values, the domain of a graph consists of all the input values shown on the x-axis. The range is the set of possible output values, which are shown on the y-axis.

For example, write, y = -1.25x + b. Substitute the first term of the first ordered pair into the same equation in place of the variable x. For example, write, y = (-1.25 x 3) + b. Substitute the second term of the first ordered pair into the same equation in place of the variable y.

Functions and Relations A relation is just a set of ordered pairs (x,y) . In formal mathematical language, a function is a relation for which: if (x1,y) and (x2,y) are both in the relation, then x1=x2 . This just says that in a function, you can’t have two ordered pairs with the same x -value but different y -values.

Overall, the steps for algebraically finding the range of a function are:

1. Write down y=f(x) and then solve the equation for x, giving something of the form x=g(y).
2. Find the domain of g(y), and this will be the range of f(x).
3. If you can’t seem to solve for x, then try graphing the function to find the range.

The range of a relation is the set of the second coordinates from the ordered pairs.

A table of values is not going to be a function if two y values have the same x value. If you run a vertical line through the x and get 2 y values, you are not dealing with a function.

A function is a rule that assigns a set of inputs to a set of outputs in such a way that each input has a unique output. A function table in math is a table that describes a function by displaying inputs and corresponding outputs in tabular form.

Determining whether a relation is a function on a graph is relatively easy by using the vertical line test. If a vertical line crosses the relation on the graph only once in all locations, the relation is a function. However, if a vertical line crosses the relation more than once, the relation is not a function.

Yes, it is a function.

If no horizontal line intersects the graph of the function f in more than one point, then the function is 1 -to- 1 . A function f has an inverse f−1 (read f inverse) if and only if the function is 1 -to- 1 .

Answer: A function is a relation in which each input has only one output. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.

A function is a relation in which each input has only one output. In the relation , y is a function of x, because for each input x (1, 2, 3, or 0), there is only one output y. x is not a function of y, because the input y = 3 has multiple outputs: x = 1 and x = 2.

Relation is the connection between people and things, or the way in which two or more different groups feel about each other or someone who is part of your family as a result of blood or marriage. …