How do you find the end behavior of #9x^4 - 8x^3 + 4x#?

1 Answer
Sep 7, 2015

Answer:

As #x##rarr##oo# #y##rarr##oo# . As #x# #rarr#-#oo#, #y# #rarr# #oo#.

Explanation:

graph{9x^4-8x^3+4x [-9.625, 10.375, -2.4, 7.6]}
Finding the end behavior is finding what happens as x goes to positive and negative infinity. On the graph, look at the two directions the graph is going: left and right (x) and up and down (y).
First lets look at what happens when x goes to positive infinity, the graph is going right (towards positive infinity) and most importantly the graph is also going up (the y values are increasing). This gives the first part of the answer. Now lets look at the negative side the x values are decreasing but the y values are increasing.

This tells us that if you keep putting in negative values the y values will keep going up, hence the second part of the answer.