SOLUTION: Please show all work. Consider the function f(x)=x^5-x^3 a Determine the behaviors as x→∞ and as x→-∞ b Find all zeros. What is the multiplicit

Algebra.Com
Question 1020077: Please show all work.
Consider the function

f(x)=x^5-x^3
a Determine the behaviors as x→∞ and as x→-∞
b Find all zeros. What is the multiplicity of roots (zeros)?
c When will the function cross the x-axis? When will it cross the y-axis?

Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
Please show all work.
Consider the function
f(x)=x^5-x^3
a Determine the behaviors as x→∞ and as x→-∞
The highest power term determins the answer::
Since x^5 goes to +oo as x goes to +oo, f(x) goes to +oo
Since x^6 goes to -oo as x goes to -oo, f(x) goes to -oo
------------------------------------------------------------------------
b Find all zeros. What is the multiplicity of roots (zeros)?
Solve x^5-x^3 = 0
x^3(x^2-1) = 0
x = 0 with multiplicity 3
x = 1 with multiplicity 1
x = -1 with multtiplicity 1
-------------------------------
c When will the function cross the x-axis?
Solve x^5 - x^3 = 0 to answer that question.
----------------
When will it cross the y-axis?
Let x = 0, then f(0) = 0
Ans (0,0)
---------------
Cheers,
Stan H.
-------------

RELATED QUESTIONS

Please show work. Consider the function f(x)=x^5-x^3 a Determine the behaviors as... (answered by ewatrrr)
Please show work Consider the function f(x)=x^5-x^3 Determine the behaviors as... (answered by Fombitz)
Consider the function f(x)=x^5-x^3 Determine the behaviors as x→∞ and... (answered by solver91311)
I am very confused with the end behavior of a Polynomial. Someone please help me with... (answered by richard1234)
For the function f(x) = -log(x) + 4, as x →∞, y→ _____. Question 5... (answered by MathLover1)
Choose the correct description of the end behavior of the function y = 0.5x A) As x... (answered by richard1234)
What is true for the following graph? Graph: http://postimg.org/image/qqy51c057/ I.... (answered by Boreal)
For the function f(x) = -4-x + 5, if x→∞, then y → ____. Question 6... (answered by MathLover1)
Help me,,, Given ∫_A▒〖[1/π(1+x^2 ) ] dx〗, where A... (answered by robertb)