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ddd [48]
3 years ago
13

Is a relation always a function? Is a function always a relation? Explain.

Mathematics
1 answer:
katen-ka-za [31]3 years ago
8 0

A function is always a relation but relation is not always a function

<u>Solution:</u>

Given that, we have to explain Is a relation always a function and is a function always a relation

Note that both functions and relations are defined as sets of lists.  

In fact, every function is a relation. However, not every relation is a function.  A relation from a set X to a set Y is called a function if each element of X is related to exactly one element in Y.

That is, given an element x in X, there is only one element in Y that x is related to.

For example, consider the following sets X and Y. Let me give you a relation between them that is not a function;

X = { 1, 2, 3 }

Y = { a , b , c, d }

Relation from X to Y : { (1,a) , (2, b) , (2, c) , (3, d) }

This relation is not a function from X to Y because the element 2 in X is related to two different elements, b and c

Relation from X to Y that is a function: { (1,d) , (2,d) , (3, a) }

This is a function since each element from X is related to only one element in Y. Note that it is okay for two different elements in X to be related to the same element in Y. It's still a function, it's just not a one-to-one function.

So, we can say that function is a type of relation.

Which means whatever a function occurs, it will be a relation from one set to other.

But when a relation occurs it may be a function but need not be always a function.

Hence, a function is always a relation but relation is not always a function.

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Step-by-step explanation:

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Area of a square = Side × Side

Side = 7x-3

Area of the square = (7x-3) × (7x-3)

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2 years ago
One year Ron had the lowest ERA (earned-run average, mean number of runs yielded per nine innings pitched)
Arada [10]

Answer:

Ron's ERA has a z-score of -2.03.

Karla's ERA has a z-score of -1.86.

Due to the lower z-score, Ron had a better yean than Karla relative to their peers.

Step-by-step explanation:

Z-score:

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this question:

Since the lower the ERA, the better the pitcher, whoever's ERA has the lower z-score had the better year relative to their peers.

Ron

ERA of 3.06, so X = 3.06

For the males, the mean ERA was 5.086 and the standard deviation was 0.998. This means that \mu = 5.086, \sigma = 0.998

So

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.06 - 5.086}{0.998}

Z = -2.03

Ron's ERA has a z-score of -2.03.

Karla

ERA of 3.28, so X = 3.28

For  the females, the mean ERA was 4.316 and the standard deviation was 0.558. This means that \mu = 4.316, \sigma = 0.558

So

Z = \frac{X - \mu}{\sigma}

Z = \frac{3.28 - 4.316}{0.558}

Z = -1.86

Karla's ERA has a z-score of -1.86.

Which player had the better year relative to their peers, Ron or Karla?

Due to the lower z-score, Ron had a better yean than Karla relative to their peers.

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Answer:

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Step-by-step explanation:

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The distance between point x and y

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