8. Give the possible values for the degree of the polynomial and the sign (+ or

Question

8. Give the possible values for the degree of the polynomial and the sign (+ or -) of the xn term.

Possible answers

Degree is even (4,6 etc); xn sign is negative

Degree is odd (3,5, etc); xn sign is positive

Can't identify degree; xn sign is positive

Degree is even (4,6, etc); xn sign is positive

Degree is even (4,6 etc); xn sign is negative

Degree is odd (3,5, etc); xn sign is positive

Can't identify degree; xn sign is positive

Degree is even (4,6, etc); xn sign is positive

8. Give the possible values for the degree of the polynomial and the sign (+ or -) of the xn term. Possible answers Degree is even (4,6 etc); xn sign is negative Degree is odd (3,5, etc); xn sign is positive Can't identify degree; xn sign is positive Degree is even (4,6, etc); xn sign is positive

Explanation / Answer

Notice the opposite ends of the graph, the extreme left and extreme right

At the extreme left, the graph is going downward

And at the extreme right, the graph is going upward

Since at the two extreme ends, the graph is going in opposite directions(upward - downward), the degree has to be an ODD VALUE

So, degree = (3 , 5 , etc)

Also, notice that on the extreme left where x ----> -infinity, the graph goes downward, i.e y ---> -infinity
So, as x ---> -inf , y ---> -inf

And similarly, as x ---> +inf , y ----> +inf

This happens only when the leading term is POSITIVE

So, our answer : Degree is odd (3,5, etc); xn sign is positive ----> ANSWER

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