Question

Describe the end behavior of the graph of the given functions.
Given: f(x)=-2x^3
22) As x-> +∞, f(x)->_____
23) As x-> -∞, f(x)->_____

Answer 1

as we plug in bigger and bigger positive values for x, this thing shoots off into - inf, you agree?

Answer 2

if so, lets consider how x^3 affects negative values:

(-1)^3 = -1 * -1 * -1
= (-1 * -1) * -1
= 1 * -1
= -1

so all negative values of x produce: -2*-x = 2x similarities

what is the value of 2(big Xs) ?

Answer 3

x^2?

Answer 4

hmm, no.

-2x^3 acts like -2x

Answer 5

the farther we move to the right, the lower we go into infinity

the farther we move to the left, the higher we go into infinity

Answer 6

would that be for every single problem or does it change for certain ones?

Answer 7

there is some adjustments to be had, but for a general rule:

\[\Large x^{~odd}\approx x\]
\[\Large x^{~even}\approx x^2\]

Answer 8

if you know the graphs for y=x, and y=x^2, youll do fine

Answer 9

so like the exponent is odd then infinity is negative?

Answer 10

the sign of the number in front plays a role: