Question

**1.** Answer the questions about the following
function.

f(x) = x + 11 / x - 9

(a) Is the point (4, - 17 /3) on the graph of f?

A. Yes, because substituting x = - 17 / 3 into the given equation results in 4.

B. Yes, because substituting x = 4 into the given equation results in - 17 / 3.

C. No, because substituting x = 4 into the given equation does not result in - 17 / 3.

D. No, because substituting x = - 17 / 3 into the given equation does not result in 4.

(b) If x = 2, f(x) = ___.

(Simplify your answer.)

Using the information in the previous step, list the point(s) on the graph of f, where x = 2.

___.

(Simplify your answer. Type an ordered pair.)

(c) If f(x) = 2, x = ___.

(Simplify your answer. Use a comma to separate answers as needed.)

Using the information in the previous step, list the point(s) on the graph of f, where f(x) = 2.

___.

(Simplify your answer. Type an ordered pair. Use a comma to separate answers as needed.)

(d) What is the domain of f?

The domain is ___.

(Type your answer in interval notation.)

(e) List the x-intercept(s), if any, of the graph of f. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. The y-intercept(s) is/are ___.

(Type an integer or a simplified fraction. Use a comma to separate answers as needed)

B. There is no y-intercept.

Answer #1

f(x)= 4x-2+3
Include on the graph the key point (as an ordered pair),
the equation of the Horizontal Asymptote, and the y-intercept (as
an ordered pair). Show Work (algebraic) for the key point or
indicate the transformation (shifts).

Consider the function
f(x)=
x3
x2 − 4
Express the domain of the function in interval notation:
Find the y-intercept: y=
.
Find all the x-intercepts (enter your answer as a
comma-separated list): x=
.
On which intervals is the function positive?
On which intervals is the function negative?
Does f have any symmetries?
f is even;f is
odd; f is periodic;None of the
above.
Find all the asymptotes of f (enter your answers as
equations):
Vertical asymptote (left):
;
Vertical...

Find all relative extrema and classify each as a maximum or
minimum. Use the second-derivative test where possible.
f(x)equals=125 x cubed minus 15 x plus 2125x3−15x+2
Identify all the relative minima. Select the correct choice
below and, if necessary, fill in the answer box to complete your
choice.
A.The relative minima are
nothing.
(Simplify your answer. Type an ordered pair. Use integers or
fractions for any numbers in the expression. Use a comma to
separate answers as needed.)
B.
There...

1a.
Find the domain and range of the function. (Enter your answer
using interval notation.)
f(x) = −|x + 8|
domain=
range=
1b.
Consider the following function. Find the composite
functions
f ∘ g
and
g ∘ f.
Find the domain of each composite function. (Enter your domains
using interval notation.)
f(x) =
x − 3
g(x) = x2
(f ∘ g)(x)=
domain =
(g ∘ f)(x) =
domain
are the two functions equal?
y
n
1c.
Convert the radian...

For the rational function
?(?)=(?+3)(?−1)(?−3)(?+1)f(x)=(x+3)(x−1)(x−3)(x+1).
Find the vertical asymptote(s):
Note: If there is more than one, use commas to separate your
answers
?=x=
Find the ?x-coordinate of each ?x-intercept:
Note: If there is more than one, use commas to separate your
answers
?=x=
Find the horizontal asymptote:
Note: If there is no horizontal asymptote, enter ‘none’
?=y=
Find the ?y-coordinate of the ?y-intercept:
?=y=
Select the correct graph of ?=?(?)y=f(x): ? Graph A
Graph B Graph C Graph D Graph E...

Consider the function below. (If an answer does not exist, enter
DNE.)
f(x) = 1/2x^(4) − 4x^(2) + 3
(a)
Find the interval of increase. (Enter your answer using interval
notation.)
Find the interval of decrease. (Enter your answer using interval
notation.)
(b)
Find the local minimum value(s). (Enter your answers as a
comma-separated list.)
Find the local maximum value(s). (Enter your answers as a
comma-separated list.)
(c)
Find the inflection points.
(x, y) = (smaller x-value)
(x, y) =...

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...

Find the equation(s) of the tangent line(s) to the graph of
the indicated equation at the point(s) with the given value of x.
xyminus13xplus16equals0; xequals4
Find the equation(s) of the tangent line(s) to the graph of
the given equation at
xequals=33.
nothing
(Type an equation. Use a comma to separate answers as
needed.)

Q 1) Consider the following functions.
f(x) = 2/x, g(x) = 3x + 12
Find (f ∘ g)(x).
Find the domain of (f ∘ g)(x). (Enter your answer using interval
notation.)
Find (g ∘ f)(x).
Find the domain of (g ∘ f)(x). (Enter your answer using
interval notation.)
Find (f ∘ f)(x).
Find the domain of (f ∘ f)(x). (Enter your answer using
interval notation.)
Find (g ∘ g)(x).
Find the domain of (g ∘ g)(x). (Enter your answer using interval
notation.)
Q...

Given the function, , state whether the
graph of the function has been reflected across the x-axis or
y-axis by filling in the blanks.
Determine if there is a reflection: Does a reflection exist in
the function? Type yes or no:
.
Determine the axis for the reflection: If there is no
reflection type N/A and if there is more than one reflection type
x,y axes. The graph has been reflected about the .
Determine the value of the exponential function....

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