Intervals, extrema and behaviot

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  (a)  1

Step-by-step explanation:

For large variable magnitude, the value of a rational function approaches the ratio of the highest-degree terms of the numerator and denominator*. Here, that is ...

  x/x = 1

f(x) approaches 1 as x approaches infinity.

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* The function approaches the line or curve defined by the quotient. (The remainder is ignored in this case.) Here, f(x) = 1 + 3/(x-3), so the quotient is the constant 1.

hello from mrbilldoesmath!

answer:

a(n) - a(n-1) -3

discussion:

this ones a bit interesting. given a(n) = 5 - 3n consider this:

a(n-1) = 5 - 3(n-1)

          = (5 - 3n) + 3             => but a(n) = 5 - 3n, the first term

          = a(n)   + 3                 => subtract 3 from both sides

a(n-1) -3 = a(n)  

or

a(n) - a(n-1) -3

you,

mrb