Question

For the rational function f(x)= (3x^3 - 27x^2 + 60x) / (2x^2 + 2x - 40) find the domain, x-intercepts, y-intercept, and vertical asymptote/ vertical asymptotes.

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.

f(x)=((2x+4)(5x+2))/((7x+8)(7x+6))
1. Find the vertical asymptote(s). If there is more than one
vertical asymptote give a list of the xx-values separated by
commas. If there are no vertical asymptotes, type in none
.
x=
2. If this function has a horizontal asymptote, give its
yy-value. If there is no horizontal asymptote, type in
none
y=
3. Find the xx-intercept(s). If there is more than one
xx-intercept give a list of the xx-intercepts separated by commas
(i.e.: (1,2),(3,4)). If there is...

Graph the quadratic function f x( ) = −2x 2 + 6x − 3. Give the
vertex, axis, x-intercepts, y-intercept, domain, range, and
intervals of the domain for which the function is increasing or
decreasing.

For the function f(x) = ? 3−1 ? 2−9 , find any slant asymptotes
and sketch the graph by finding any vertical asymptotes, horizontal
asymptotes, x intercepts, y intercept.

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.

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).

Find the vertical asymptotes, horizontal asymptote, and x and y
intercepts of the following function and sketch a graph
f(x) = (x^2 − 4) / (x^2 − 2x − 15)

Show work please
1. Find the slant asymptote f(x)=(x^2-4)/(x-1)
2. Consider the rational function f(x)=(x^2-1)/(x^2+x-6)
a. The equations of the vertical asymptotes
b. The equation of the horizontal asymptote
c. The derivative of the function
d. Critical point(s)
e. Extrema, justify your answers

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...

Analyze the function f and sketch the curve of f by hand.
Identify the domain, x-intercepts, y-intercepts, asymptotes,
intervals of increasing, intervals of decreasing, local maximums,
local minimums, concavity, and inflection points. f(x) = 3x^4 −
4x^3 + 2

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