Which of the following sets of ordered pairs represents a function?

1 answer:

3 0

{(-1,3),(-1,4),(-1,5),(-1,6)} is the set from the given question which is a set of ordered pairs representing a function.

<h3>What is ordered pair?</h3>

An ordered pair (a, b) in mathematics is a group of two things. The pair's order of objects matters because the ordered pair (a, b) differs from the ordered pair (b, a) unless a = b. (By contrast, an unordered pair of a and b equals an unordered pair of b and a.)

Ordered pairs are also known as 2-tuples, or sequences (or, in computer science, occasionally, lists) of length 2. Sometimes referred to as 2-dimensional vectors, ordered pairs of scalars. Technically speaking, this is a misuse of the term because an ordered pair need not be a component of a vector space. An ordered pair's entries may be other ordered pairs, allowing for the recursive definition of ordered n-tuples (ordered lists of n objects).

Learn more about ordered pairs

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Patrick has just finished building a pen for his new dog. The pen is 3 feet wider than it is long. He also built a doghouse to p

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General Idea:

(i) Assign variable for the unknown that we need to find

(ii) Sketch a diagram to help us visualize the problem

(iii) Write the mathematical equation representing the description given.

(iv) Solve the equation by substitution method. Solving means finding the values of the variables which will make both the equation TRUE

Applying the concept:

Given: x represents the length of the pen and y represents the area of the doghouse

<u>Statement 1: </u>"The pen is 3 feet wider than it is long"

$Length \; of\; the \; pen = x\\ Width \; of\; the\; pen=x+3$

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<u>Statement 2: "He also built a doghouse to put in the pen which has a perimeter that is equal to the area of its base"</u>

$Area \; of\; the\; Dog \; house=y\\ Perimeter \; of\; Dog\; house=y$

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<u>Statement 3: "After putting the doghouse in the pen, he calculates that the dog will have 178 square feet of space to run around inside the pen."</u>

$Area \; of \; the\; Pen - Area \;of \;the\;Dog \;House=\;Space\;inside\;Pen\\ \\ x \cdot (x+3)-y=178\\ Distributing \;x\;in\;the\;left\;side\;of\;the\;equation\\ \\ x^2+3x-y=178\Rightarrow\; 1^{st}\; Equation\\$

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<u>Statement 4: "The perimeter of the pen is 3 times greater than the perimeter of the doghouse."</u>

$Perimeter\; of\; the\; Pen=3\; \cdot \; Perimeter\; of\; the\; Dog\; House\\ \\ 2(x \; + \; x+3)=3 \cdot y\\ Combine\; like\; terms\; inside\; the\; parenthesis\\ \\ 2(2x+3)=3y\\ Distribute\; 2\; in\; the\; left\; side\; of\; the\; equation\\ \\ 4x+6=3y\\ Subtract \; 6\; and \; 3y\; on\; both\; sides\; of\; the\; equation\\ \\ 4x+6-3y-6=3y-3y-6\\ Combine\; like\; terms\\ \\ 4x-3y=-6 \Rightarrow \; \; 2^{nd}\; Equation\\$