consider the leading term of polynomial function. what is the end behavior of the graph -3x^5+9x^4+5x^3+3

Question

ganeshie8 · Answer

whats the leading term here ? :)

ybarrap · Answer

When x is very very very big, which term is bigger than all the others, in terms of magnitude. The point of this is to show that this very term is the one that "dominates" the others in terms of its magnitude and so you can just ignore the others. Once you have this, if this term you've identified is positive, then  it (and the whole function) goes off into  positive infinity. However, if it is negative, it goes off into negative infinity.

The reason all this is important is because it will tell you where the WHOLE function will go when x is large and its entirely dictated by this term. Note that there are only 4 terms that you need to consider, -3x^5,9x^4,5x^3 and 3. One of these is key (Hint: The one with the highest degree will "dominate").