Question

Graph: f(x)= 2

Find (a) The domain of f.

(b) All asymptotes (write the equations)

(c) X- intercept(s), Y- intercept. Write them as ordered pairs.

(d) Graph the function. Include asymptotes

Answer #1

consider the funtion f(x)=3x-5/sqrt x^2+1. given
f'(x)=5x+3/(x^2+1)^3/2 and f''(x)=-10x^2-9x+5/(x^2+1)^5/2
a) Find the domain of f. (write in interval notation):
Df:=_____________?
b) Find the x- and y- intercepts. if any. (write your answers as
ordered pairs).
c) Find the asymptotes of f, if any. If there are not, write
why. (write answers as equations).
d) Find all of the critical numbers of f. on what intervals is f
increasing/decreasing?
show all work

11) Let p(x) = (4x^2-9)/(4x^2-25)
(a) What is the domain of the function p(x)?
(b) Find all x- and y-intercepts.
(c) Is function p(x) an even or odd function?
(d) Find all asymptotes.
(e) Find all open intervals on which p is increasing or
decreasing.
(f) Find all critical number(s) and classify them into local
max. or local min..
(g) Sketch the graph of p. [Please clearly indicate all the
information that you have found in (a)–(f) above.]

Given the polynomial function f (x) = (x + 3)(x + 2)(x −1)
(a) Write all intercepts as ordered pairs
(b) Find the degree of f to determine end behavior (c) Graph the
function. Label all intercepts

Sketch the graph of the function f(x) = x − 4 / x + 4 using the
guidelines below, a. Determine the domain of f.
b. Find the x and y intercepts.
c. Find all horizontal and vertical asymptotes.
d. Determine the intervals of increasing/decreasing.
e. Determine the concavity of f.

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

a) Find the domain and range of the following function:
f(x,y)=sin(ln(x+y))
b) sketch the domain.
c) on seperate graph, sketch three level curves

f (x) = ex/x2
Find the Domain of f(x)
Does the function have x- or y- intercept of
f(x)?
Find the vertical and horizontal asymptotes.
Find f'(x) and f''(x) .
Find the critical points, find the interval where f(x) is
increasing and decreasing, the interval where f(x) is concave up
and down and the inflection points.

find a function whose graph has the given asymptotes
x=-8, x=3, and y=8
a) f(x)= 8x^2 / x^2+5x-24
b) f(x)= 8x^2 / x^2-5x-24
c) f(x)= x^2+8 / x^2+5x-24
d) f(x)= x^2+8 / x^2-5x-24

Please find all of horizontal asymptotes and vertical asymptotes
of function f(x) = [−7x^2 * (x − 2)^2 ]/ [ 3(x + 1)^3 * (x −
2)]

consider the following function f(x)=x2-3x/x2-4x+3
find all x inter and the equations of all vertical
asymptotes

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