In: Math

Given: f(x) = x 2−36 x 2−7x+6 Find the following

a. V.A.

b. Domain

c. H.A.

d. X-intercept

e. Y-intercept

f. Graph

we are given function as

**(A)**

we can factor top and bottom

now, we can set bottom =0

and then we can solve for x

so, VA is
**.........Answer**

**(b)**

**Domain:**

It is all possible values of for which any function is defined

this function is undefined when bottom =0

so, we get domain as

**(c)**

we can see that

degree of top =2

degree of bottom =2

both degrees are equal

so, HA will be ratio of their leading coefficients

so, we get

**(d)**

**x-intercept:**

we can set f(x)=0

and then we can solve for x

**(e)**

**y-intercept:**

we can plug x=0

**(f)**

we can draw graph

Let f(x) = x / (4−x^2) .
(a) Find the domain and intercepts of f(x).
(b) Find all asymptotes and limits describing the end behavior
of f(x).
(c) Find all local extrema and the intervals on which f(x) is
increasing or decreasing.
(d) Find the inflection points and the concavity of f(x).
(e) Use this information to sketch the graph of f(x)

Given f''(x)= 4x-6
and f'(-2)=5 and f(-2)=1
FIND: Find f'(x)=
and find f(2)=

The function f(x)=3x+2 is one-to-one
a) find the inverse of f
b) State the domain and range of f
c) State the domain and range of f-1
d) Graph f,f-1, and y=x on the same set of axes

Find the domain for each function please explain. f(x)=10x^2 + x
f(x)= -2/x^2

How do you find the domain of:
f(g)= 5x^2+4
f(g)= 3x; -2<x<6
f(g)= (1) / 3x-6
f(g)= (x+2) / x^2-1
f(g)= x^4 / x^2+x-6
f(g)= sqrt (x+1)
f(g)= sqrt (x^2+9)

Find f(x) for the following function. Then find f(6), f(0), and
f(-7).
f(x)=-2x^2+1x
f(x)=
f(6)=
f(0)=
f(-7)=

let f(x)=(x^2 + 2x) / (x - 1)^2
a) Find the domain and if any intercepts
b)find the horizontal asymptotes
c) find the vertical asymptotes
d)find the intervals on which the function is increasing and
decreasing and identify the function's local extreme values,
critical values
e)identify the concavity and if any the point of inflection
f) graph the function

5. Consider the function f(x) = -x^3 + 2x^2 + 2.
(a) Find the domain of the function and all its x and y
intercepts.
(b) Is the function even or odd or neither?
(c) Find the critical points, all local extreme values of f, and
the intervals on which f is increasing or decreasing.
(d) Find the intervals where f is concave up or concave down and
all inflection points.
(e) Use the information you have found to sketch...

6) Given: (a) f (x) = (2x^2)/(x^2 −1) - Calculate f ′(x) and f
″(x) - Determine any symmetry - Find the x- and y-intercepts - Use
lim f (x) x→−∞ and lim f (x) x→+∞ to determine the end behavior -
Locate any vertical asymptotes - Locate any horizontal asymptotes -
Find all intervals where f (x) is increasing and decreasing - Find
the open intervals where f (x) is concave up or concave down

(6) Consider the function f(x, y) = 9 − x^2 − y^2 restricted to
the domain x^2/9 + y^2 ≤ 1. This function has a single critical
point at (0, 0)
(a) Using an appropriate parameterization of the boundary of the
domain, find the critical points of f(x, y) restricted to the
boundary.
(b) Using the method of Lagrange Multipliers, find the critical
points of f(x, y) restricted to the boundary.
(c) Assuming that the critical points you found were...

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