Question
Watch the video and then solve the problem below. Use the leading coefficient test to determine whether y rightarrow infinity or y rightarrow -infinity as x rightarrow infinity and as x rightarrow -infinity. y = x^5 - 4x^3 + 4x Choose the correct answer below. A. As x rightarrow infinity, y rightarrow infinity, and as x rightarrow, - infinity, y rightarrow, infinity. B. As x rightarrow infinity y rightarrow - infinity, and as x rightarrow - infinity, y rightarrow -infinity. C. As x rightarrow infinity, y infinity -infinity, and as x rightarrow - infinity, y rightarrow infinity. D. As x rightarrow infinity, y rightarrow infinity, and x rightarrow -infinity, y rightarrow -infinity.
Explanation / Answer
ANS: Here the leading coefficient is 1 that is positive and degree of function is 5 so it's odd.
For odd function with positive leading coefficient the graph rises to right and falls to left (for remembering purpose you can remember the simple graph of y = x) so as x goes to + graph moves to right and rises so y will be +
As x goes to left that is - graph fall to -.
NOTE: represents infinity.