Question

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.

Answer #1

An x intercept at x = -2 and 5 means the numerator has a zero at x = -2 and x=5

The rational function f that has a vertical asymptote at x = 3 and x=6, then the denominator of the rational function contains the term (x - 3) and (x-6).

So the rational function with x-intercepts –2 and 5, y-intercept 5, and vertical asymptotes x = 3 and x = 6

.

The horizontal asymptote of the graph of the function

is since both polynomials are the same degree, divide the coefficients of the highest degree terms

i.e The horizontal asymptote is at .

1. find all vertical asymptotes of function f(x) =
In((e^2In(x))-5x+6)
2. find all x intercepts of the function
g(x)=In((e^2In(x))-3x+5)-In(2)-In(3/2)

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...

Give an example of a rational function f whose graph has the
following properties.
vertical asymptote: x = 2
horizontal asymptote: y = 1
x-intercept: (5, 0)

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

1. You are given the function f(x) = x/(1−x)
a) Find the x and y- intercepts.
b) Find the horizontal asymptote(s).
c) Find the vertical asymptote(s) and do a limit analysis of the
behavior of f on either
side of each vertical asymptote.
d) Find the critical number(s) of f.
e) Find the interval(s) of increase and decrease of f.
f) Find the relative maximum and minimum value(s) of f.
g) Find the hypercritical number(s) of f.
h) Find the...

1. Graph of the function and label any intercepts and
asymptotes.
R(x)= x+5/x(x-3)

For the function
f(x) =x(x−4)^3
•
Find all
x-intercepts and find the
y-intercept
•
Find all critical numbers,
•
Determine where the function is increasing and where it is
decreasing,
•
Find and classify the relative extrema,
•
Determine where the function is concave up and where it is
concave down,
•
Find any inflection points, and Use this information to sketch
the graph of the function.
•
Use this information to sketch the graph of the function.

Let f (x) = 4X^2 -9 /X^2-16
(a) State the y-intercept
. (b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.

Graph the equation ?? = ??^2????6/2??^2?2 by hand. find and show
the algebra to find the EQUATIONS of the vertical asymptote(s),
horizontal asymptote (if there is one), as well as the x and y
intercepts.

f(x) Write a formula or
describe a method for identifying each of these characteristics of
f(x).
a) x-intercepts
b) y-intercepts
c) vertical asymptotes
d) horizontal asymptotes
e) holes in the graph
f) intervals where f(x) is positive or
negative
g) Describe f(x) if the horizontal asymptote is
y 0.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 5 minutes ago

asked 6 minutes ago

asked 7 minutes ago

asked 7 minutes ago

asked 7 minutes ago

asked 8 minutes ago

asked 11 minutes ago

asked 11 minutes ago

asked 14 minutes ago

asked 14 minutes ago

asked 15 minutes ago