Question

Find a rational function with vertical asymptotes x=3 and x=1, horizontal asymptotes y=2, zeros are 5,2, and -1 and y-intercept is (0,1).

Answer #1

Find a rational function with x-intercepts –2 and 5, y-intercept
5, and vertical asymptotes x = 3 and x = 6. State the horizontal
asymptote of the graph of the function.

Write the equation of a rational function with the following
characteristics: Vertical asymptotes at x = 3 and x = -4, a
horizontal asymptote at y = 0, no x-intercepts and a y-intercept at
(0, 1/6).
Consider the polynomial q(x) = 3x2 - 11x2
+ kx + 8. Given that q(x) has a factor (x - 4), find the value of
k:
Hence or otherwise, factorize q(x) as a product of linear
factors.

Graph f(x)=
x3-x2-16x+16/2x2-18
List and mark the vertical and horizontal asymptotes, oblique
asymptotes, zeros, and y- intercepts on the graph.

r(x)= x^2+4x+3 divided by (x-5)(x-2)(x+3)
a. determine the domain of r(x)
b. determine the zeros, vertical asymptotes and holes
c. determine the y intercept of r(x)
d. determine the equation of the horizontal asymptote of
r(x)

For the rational function
?(?)=(?+3)(?−1)(?−3)(?+1)f(x)=(x+3)(x−1)(x−3)(x+1).
Find the vertical asymptote(s):
Note: If there is more than one, use commas to separate your
answers
?=x=
Find the ?x-coordinate of each ?x-intercept:
Note: If there is more than one, use commas to separate your
answers
?=x=
Find the horizontal asymptote:
Note: If there is no horizontal asymptote, enter ‘none’
?=y=
Find the ?y-coordinate of the ?y-intercept:
?=y=
Select the correct graph of ?=?(?)y=f(x): ? Graph A
Graph B Graph C Graph D Graph E...

Function: H(x)= 7x^3-117x^2+535x-325
A. Use Rational Zeros Theorum to find all possible rational
zeros.
B. Find the actual rational zero and prove it is zero by using
synthetic division.
C. Find the remaining zeros.
D. Factor H(x) completely into linear factors.

F(x) = ( (x+3)/(x+1) )2
find the domain of F
and any critical numbers, horizontal asymptotes, vertical
asymptotes and points of inflection

Let g (x) = [(x^2-3)/(x^3)]
(a) Determine (if they exist) the vertical and horizontal
asymptotes of g.
(b) Find the formula for g′ (x) and g′′ (x).
(c) Find (if they exist) the local extremes of g.
(d) Find (if they exist) the inflection points of g.
(e) Determine the intervals where g is increasing, and where g
is decreasing.
(f) Determine the intervals where g is concave upward, and
where g is
concave down.
(g) Plot the graph of...

do quadratic and rational functions always have vertical and
horizontal asymptotes?

f(x) = 1/(x-2) + x - 2
a) Find the vertical and horizontal asymptotes.
b) Find the intervals of increase or decrease.
c) Find the local maximum and minimum values.
d) Find the intervals of concavity and the infection points.
I need help with parts b and d. Step-by-step solutions would be
very much appreciated. Thank you for the help in advance!

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