SOLUTION: Let f(x) = x^4 + 2x/x^2 − 1
.
(a) Determine the domain of f. I got x cannot equal 1 and -1
(b) Determine all zeros of f: i cant find this i set the whole expression to zer
Algebra.Com
Question 1025032: Let f(x) = x^4 + 2x/x^2 − 1
.
(a) Determine the domain of f. I got x cannot equal 1 and -1
(b) Determine all zeros of f: i cant find this i set the whole expression to zero and multiplied x^2-1 from both sides leaving me with x^4+2x n ow what do i do?
(c) Determine all vertical asymptotes of f: this is x= 1 or x=-1
(d) Determine the y-intercept of f: there is no horizontal asymptotes
(e) Determine the long range behaviour of f? I don't understand this will you be to please help me.
Thank you for all your time!
Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Almost assuredly you mean f(x)=(x^4+2x)/(x^2-1).
The numerator and denominator have no factor in common.
Roots and undefined x values will determine intervals on the x-axis. This affects domain.
ZEROS
Look in the numerator.
x is a zero.
also would be a root.
or .
This root or zero is .
VERTICAL ASYMPTOTES
These occur at x=1 and x=-1 because f is not defined for those values. Why? Because the denominator must never become 0.
CRITICAL x VALUES
These are the x values of , -1, 0, 1.
y-INTERCEPT
Let x be 0. What is y?
.
That should all be very helpful for you, although not everything was completed for you.
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