Question

Problem 3.2.60

Using f(x) = -x^2(x + 2)(x - 2) determine the following:

(a) Use the Leading Coefficient Test to determine the graphs end
behavior.

(b) Find the x-intercepts. State whether the graph crosses the
x-axis, or touches

the x-axis and turns around, at each intercept.

(c) Find the y-intercept.

(d) Determine whether the graph has y-axis symmetry, origin
symmetry, or neither.

(e) If necessary, find a few additional point and graph the
function. Use the

maximum number of turning points to check whether it is drawn
correctly.

Answer #1

Using f(x) = x^4 - x^2 determine the following:
(a) Use the Leading Coeefficient Test to determine the graphs end
behavior.
(b) Find the x-intercepts. State whether the graph crosses the
x-axis, or touches
the x-axis and turns around, at each intercept.
(c) Find the y-intercept.
(d) Determine whether the graph has y-axis symmetry, origin
symmetry, or neither.
(e) If necesary, find a few additional point and graph the
function. Use the
maximum number of turning points to check whether...

given the polynomial function f(x)=x^2(x-3)(x+1)
find x and y intercepts of f(x) and determine whether the
graph of f crosses or touches the x-axis at each x-intercept.

Determine whether the graph is that of a function. If it
is, use the graph to find its domain and range, the intercepts, if
any, and any symmetry with respect to the x -axis, the y-axis, or
the origin.

Lef f(x) = -(x+4)(x-1)^3(x-3)^2 = -x^6 + 5x^5 + 6x^4 - 74x^3 +
151x^2 - 123x + 36
1.)Determine the end behavior
2.) Find the real zeros of f(x) & state the multiplicity of
each zero. Determine the manner in which the graph of f(x) crosses
or touches the x-axis at each zero.
3.) Find the x-intercepts and the y-intercept
4.) Draw the graph of f(x)
Please show work for answers- thanks :)

For the equation
?f(x)equals=x squared minus 2 x minus 15x2?2x?15?,
?a) determine whether the graph of the given
quadratic function opens up or? down, ?b) find
the? vertex, ?c) find the axis of? symmetry,
?d) find the? x- and? y-intercepts, and
?e) sketch the graph of the function.

Answer all the following
1a.
Find any intercepts. (Order your answers from smallest to
largest x, then from smallest to largest y.)
y = x2 − 9x + 18
y-intercept
(x, y) =( , )
x-intercepts
(x, y)= ( , )
(x,y)= ( , )
1b.
Test for symmetry with respect to each axis and to the origin.
(Select all that apply.)
y = x2 + 5x
The equation is symmetric with respect to the
x-axis.
The equation is symmetric...

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:...

5. [20 pts] For the function ?(?) = (4?−8)/(?^2−?−6) answer the
following to sketch the graph. Do not use a graphing
calculator.
a. [2 pts] Determine the domain of the function, write your
answer in interval notation:
b. [4 pts] Find the x-intercept(s), if any.
c. [2pts] Find the y-intercept, if any.
d. [2 pts] Find the vertical asymptotes, if any.
e. [2 pts] Find the horizontal asymptote(s) or slant asymptote,
if any.
f. [4 pts] Determine whether the graph...

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.

Consider the quadratic function f, given by f(x) = −x2 + 6x−8.
(i) Determine if the graph of y = −x2 + 6x − 8 is concave up or
concave down, providing a justiﬁcation with your answer. (ii)
Re-write the equation of the quadratic function f, given by f(x) =
−x2 +6x−8, in the standard form f(x) = a(x−h)2+k by completing the
square. Hence determine the vertex of the graph of y = f(x).
(iii) Identify the x-intercepts and y-intercept...

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