Question

1. Given ?(?) = √? − ? and ?(?) = ? + ?. Find the following:

a) The domain of ?(?). Write the answer in interval notation.

b) (? ∘ ?)(?)

c) The domain of (? ∘ ?)(?)

2. Let ?(?) = ??? − ??. Find the difference quotient

3. For the given function: ?(?) = ? ? + ?? − ??

(a) Rewrite the function in the vertex form by COMPLETING THE SQUARE. (standard form of quadratic function, you may use the short cut)

(b) State the vertex and axis of symmetry.

Answer #1

1. Given the following quadratic function: f(x)=4x2-12x+5
a. Use the method of completing the square to rewrite the
equation of f
b. What are the coordinate of the vertex of f
c. What are the zeros of f (ker(f))
d. What is the image of f (image(f))
e. Describe the simple transformations that take x2 to f(x)

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...

1- If
?(?)=3?5?+29?5?+1
find the inverse function.
2- State the domain of the function ?(?)=8?−94?
3- State the domain of the function ?(?)=5?−83?+5 in interval
notation
4- State the domain of the function ?(?)=7?−8?−3
in interval notation.
5- State the domain of the function ?(?)=9?+1?2−3?−40
in interval notation
6- State the domain of the function ?(?)=8?+13?2−11?+8
in interval notation.
7- State the domain of the function ?(?)=8?−39?2+12?+13
in interval notation.

Find each of the following functions. f(x) = 4 − 4x, g(x) =
cos(x)
(a) f ∘ g and State the domain of the function. (Enter your
answer using interval notation.)
(b) g ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(c) f ∘ f and State the domain of the function. (Enter your
answer using interval notation.)
(d) g ∘ g and State the domain of the function. (Enter your
answer using...

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....

Using interval notation, determine the largest domain over which
the given function is one‑to‑one. Then, provide the equation for
the inverse of the function that is restricted to that domain.
If two equally large domains exist over which the given function
is one‑to‑one, you may use either domain. However, be certain that
the equation for the inverse function you submit is appropriate for
the particular domain you choose.
f(x)=10−x
(Give your answer as an interval in the form (∗,∗).
Use...

Given the rational function h(x) = (x^3 +5x^2-2x-24)/(x^2-9),
find the following information
a. Use your knowledge of polynomials to factor the numerator and
the denominator of h(x) to rewrite the function in a different
form.
b. Use long division to find the quotient and the remainder to
rewrite h(x) in a different form.
c. What is the woman of h?
d. Identify the vertical asymptotes.
e. Determine the exact location of any removable discontinuity
if one exists.

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.

1.) Find the standard form of the equation of the parabola with
the given characteristic(s) and vertex at the origin.
Horizontal axis and passes through the point (−4, 7)
2.) Find the standard form of the equation of the parabola with
the given characteristics.
Vertex: (5, 1); focus: (3, 1)

Find the standard form of the equation of the ellipse with the
given characteristics. Center: (2, 3); vertex: (−6, 3); minor axis
of length 14

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