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9. A relation contains the points ( -5,-10),( -2,-4)(-1,-2),(4,8) and (5,10) . Is this a function? Explain. (2 points)

User Naveejr
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1 Answer

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Answer:

Yes it is a function given by f(x) = 2x

Explanation:

Any function can approximated as series or a polynomial. For example,


e^(x) = 1 + (x)/(1!) + (x^(2))/(2!) + (x^(3))/(3!) ... (exponential function)

(n! or n factorial is equal to n(n-1)(n-2)...3.2.1 ; 3! = 3.2.1 = 6)

and for the series to converge(the sum does not go to infinity), higher order terms must tend to zero.

General form of a polynomial/series:
f(x) = a + bx +cx^(2) + ...

For the given set of points, we can start with the straight line equation:


f(x) = y = a + bx ........(1)

Let us take two points from the given relation: (-5, -10), (-1, -2)

and put the respective x and y values in equation (1), we get two equations, which we can then solve simultaneously to get values of
a and
b:


-10=a-5b ........(2)


-2=a-b ..........(3)

Now (3) - (2) gives us:
b=2 and putting the value of
b in any of the above equation gives us
a=0

Hence, we get the equation,
f(x)=y=2x

It can be seen that all the given points satisfies this relation and since we get a unique
y for every
x, we can call this a function.

User ErikL
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