Question

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 interval(s) of upward and downward concavity of f.

I) Find the point(s) of inflection of f.

j) Sketch the graph of f.

Answer #1

Let f(x)= (x-2)/(x^2-9)
A. find the x and y-intercepts
B. find the vertical and horizontal asymptote if any
C. find f'(x) and f''(x)
D. find the critical values
E. determine the interval of increasing, decreasing, and find
any relative extreme
F. determine the interval which f(x) is concave up, concave
down, and any points of inflection

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)

(i) Given the function f(x) = x3 − 3x + 2
(a) What are the critical values of f?
(b) Find relative maximum/minimum values (if any). (c) Find
possible inflection points of f.
(d) On which intervals is f concave up or down?
(e) Sketch the graph of f.
(ii) Find a horizontal and a vertical asymptote of f(x) = 6x .
8x+3

Given f(x) = , f′(x) = and f′′(x) = , find all possible
x2 x3 x4
intercepts, asymptotes, relative extrema (both x and y values),
intervals of increase or decrease,
concavity and inflection points (both x and y values). Use these
to sketch the graph of f(x) = 20(x − 2)
.
x2

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)=(x^2)/(x-2) Find the following
a) Domain of f
b) Intercepts (approximate to the nearest thousandth)
c) Symmetry (Show testing for symmetry)
d) asymptotes
e) Intervals of increase/decrease (approximate the critical
numbers to the nearest thousandth. Be sure to show the values
tested)
f) Local maxima and local minima
g) Intervals of concavity and points of inflection (be sure to
show all testing)
h) summary for f(x)=(x^2)/(x-2)
Domain
X intercepts:
Y intercept:
symmetry:
asymptote:
increasing:
decreasing:
local max:
local min:...

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.

Find the horizontal intercepts, the vertical intercept, the
vertical asymptotes, and the horizontal or slant asymptote of the
function. Use that information to sketch a graph.
g(x) = x-5/3x-1

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

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.

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