Is the following relation a function?
2 answers:
<h2>Answer:</h2>
Yes, the given relation is a function.
Because every element of the set x has a single image.
<h2>Step-by-step explanation:</h2><u>Relation--</u>
A relation from the set A to set B is the collection or set of all the ordered pair of the type: (a,b)
where a belongs to A and b belongs to B.
<u>Function--</u>
A relation from a set A to set B is a function if every element of A is mapped to some element of B and there is just one image corresponding to each element of x.
Now after looking at the mapping diagram we observe that no element of A is mapped to two elements of B.
i.e. every element has a single image.
Hence, the relation is a function.
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<h2>Answer:</h2>
Figure B
<h2>Step-by-step explanation:</h2>The Pythagorean Theorem is , where c is the longest side of the triangle (the hypotenuse).
To find the side length of each square, you have to square root the area of each square. This means that Figure A has side lengths of 3, 6 and 8 units. Figure B has side lengths of 5, 12 and 13 units.
In Figure A, if the triangle is right-angled, the equation must be correct. 9 + 36 = 45. 45 is not equal to 64, so the triangle is not right-angled.
In Figure B, if the triangle is right-angled, the equation must be correct. 25 + 144 = 169. 169 is 13 squared, so the triangle is right-angled.
Alternatively, as you are already given the square values for each side length, there is no need to square root and square again. You can just test if the two smaller areas equal the larger area, but the explanation above uses a more detailed example of the Pythagorean Theorem.