Expert: Sherry Wallin - 9/18/2009

Question
without graphing,m describe the end behavior of the graph of the functions:

f(x) = 3x^3

g(x) = 2x^5-4x

h(x) = -2x^4

Answer
These questions can be analyzed simply:

for f(x) when x gets large what happens to x^3? It gets very large in either the negative or positive direction so the graph goes to negative infinity and to positive infinity.

for g(x), which has more effect on the value of g(x) in the expression 2x^5 -4x? Hopefully you can see that x^5 is going to get bigger much faster than 4x and so at some point the 4x has relatively little to do with the graph so we say that the x^5 dominates the graph, so again g(x) gets large in both the positive and negative directions. Both of these problems get large in both directions because they are odd powers.

Now h(x) is different in that it has an even power so no matter what x is x^4 will be positive but h(x) is being multiplied by a negative number, precisely -2 so this graph will get very large in the negative infinity direction.

I hope I have explained this in a way that makes sense to you. Please let me know if you need further explanation.

Math Prof