Question

What is the end behavior of the function f(x) = -3x4-x3 + 2x2 + 4x + 5?

Answer 1

Which of the following represents the zeros of f(x) = 6x3 - 29x2 - 6x + 5?

-5, one-third, one-half

5, -one-third, one-half

5, one-third, - one-half

5, one-third, one-half

Answer 2

1) Please identify the term that has the highest power of x.
2) Drop the coefficient of that term and do a quick sketch of the function that results.
a) If, for example, the resulting function is y=x^2, the graph of this function will decrease, starting on the extreme left and moving to the right, and increase once you've passed x=0. This is an example of how to describe "end behavior" for y = x^2.
b) if y=x^3, and we move from left to right as before, y is constantly increasing EXCEPT at x=0). In other words, the graph begins in quadrant 3 and ends in quadrant 1.
Determine the "end behavior" of the highest-powered term of the given function.
3) Determine how the negative coefficient (-3) of the highest power of x in the given equation will affect the "end behavior" analysis.
4) Describe the end behavior of the given function, mentioning the apprpriate quadrants and the convention that we are moving from left to right.

Answer 3

What is the end behavior of the function f(x) = -3x4-x3 + 2x2 + 4x + 5?

Up on the left, up on the right

Up on the left, down on the right

Down on the left, up on the right

Down on the left, down on the right

Answer 4

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