The ordered pairs (1,36), (2, 49), (3,64). (4, 81). and (5, 100) represent a function. What is a rule that represents this function?

Answer 1

Rule is #n^(th)# ordered pair represents #(n,(n+5)^2)#

In the ordered pairs #(1,36), (2, 49), (3,64). (4, 81)#. and #(5, 100)#, it is observed that

(i) first number starting from #1# is in arithmetic series in which every number increases by #1#, i.e. #d=1#

(ii) second number are squares and starting from #6^2#, it goes on to #7^2#, #8^2#, #9^2# and #10^2#. Observe that #{6,7,8,9,10}# to increase by #1#.

(iii) Hence while first part of first ordered pair starts from #1#, its second part is #(1+5)^2#

Therefore, the principle that embodies this role is that

#n^(th)# ordered pair represents #(n,(n+5)^2)#

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Answer 2

Julia Adams

The rule that represents this function is ( f(x) = x^2 + 35 ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.