Questions on Algebra: Functions, Domain, NOT graphing answered by real tutors!

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Question 1035218: consider the function f(x)= (1-x^2)/(1+x^2)^2
Over which intervals is f(x) increasing?
Choices: A(-√3,0) B(-1,0) C(-√3,0)U(√3,∞) D(-∞,-√3)U(√3,∞) or E, None of these.
Please help. This is the only one I can't get as I'm preparing for my final.
Click here to see answer by robertb(5830)

Question 1035303: A function is defined as
f(x)=4x^2+1. If the graph of this function shifts 4 units down, 5 units right, and is reflected across the x-axis, what is the coordinate for the vertex of the resulting function.
A (5, -3)
B (5, 3)
C (4, 5)
D (0, 1)

Click here to see answer by stanbon(75887)

Question 1035316: Jess has a summer job at a day care. She earns $8.50 an hour, but never works more than 20 hours in a week. Her salary can be modeled by the function s = 8.5h.
She decided that s < 170 could represent the domain of her situation.
Do you agree? Why or Why not?
Click here to see answer by richwmiller(17219)

Question 1035300: 21. A function is defined as
f(x)=4x^2+1. If the graph of this function shifts 4 units down, 5 units right, and is reflected across the x-axis, what is the coordinate for the vertex of the resulting function.
A (5, -3)
B (5, 3)
C (4, 5)
D (0, 1)

Click here to see answer by josgarithmetic(39618)

Question 1034888: Given that f(x)=5x-3, calculate
f◦f(-1)=
Given that g(x)=4-x^2, calculate
g◦g(4)=
Click here to see answer by robertb(5830)

Question 1035418: find the average rate of change of f(x)=x^3-2x+6: from -6 to -4
Click here to see answer by Alan3354(69443)

Question 1035498: Determine the coordinates of the point of intersection of g and its inverse algebraically
Click here to see answer by ikleyn(52794)

Question 1035754: Find a formula for a quadratic function with leading coefficient 1, whose graph has zeros at x = 3 and x = 5.
f(x)=
Click here to see answer by fractalier(6550)

Question 1035754: Find a formula for a quadratic function with leading coefficient 1, whose graph has zeros at x = 3 and x = 5.
f(x)=
Click here to see answer by Alan3354(69443)

Question 1035753: Find a formula for a quadratic function with leading coefficient 1, whose graph has zeros at x = 3 and x = 5.
f(x)=
Click here to see answer by fractalier(6550)

Question 1035749: Find a formula for a quadratic function with leading coefficient 1, whose graph has zeros at x = 3 and x = 5.
f(x)=
Click here to see answer by fractalier(6550)

Question 1035748: Find a formula for a quadratic function with leading coefficient 1, whose graph has zeros at x = 3 and x = 5.
f(x)=
Click here to see answer by Alan3354(69443)

Question 1035748: Find a formula for a quadratic function with leading coefficient 1, whose graph has zeros at x = 3 and x = 5.
f(x)=
Click here to see answer by fractalier(6550)

Question 1035762: For what value of the domain (-3,-1,0,2,5) does f(x) = g(x)

Click here to see answer by fractalier(6550)

Question 1035917: 7 2/3 + n = 9 1/2
Click here to see answer by ashishtayal(3)

Question 1035958: What are the zeros of this function linked in the graph below?
Graph: http://postimg.org/image/4rk8tiyt7/
ty
Click here to see answer by josgarithmetic(39618)

Question 1035959: For the function in this chart, which values of x has a relative minima or maxima?
x f(x)
-3 -2
-2 2
-1 0
0 -2
1 2
2 18
3 52
Either
-3 and 3
-3, 0, and 3
-2 and 0
2 and �-2
Click here to see answer by robertb(5830)

Question 1036050: What is the probability that out of 400 babies born, 205 or fewer will be girls? Assume that boys and girls are equally probable, and round your answer to the nearest tenth of a percent.
Click here to see answer by Boreal(15235)

Question 1036152: Below in the function chart, between what x values would you find the zeros of the function?
x f(x)
-3 73
-2 8
-1 -7
0 -8
1 -7
2 8
3 73
A.) -1 and 0, 0 and 1
B.) -2 and �-1, 1 and 2
C.) -7 and 8, �-8 and �-7
D.) 1 and �-1
Click here to see answer by robertb(5830)

Question 1036393: Let f(x) = x√x − 2√(x + 3)
b) What is the slope of the tangent line to the graph of f when x = 1?
c) What is the rate of change of the function f at x = 1?
I have already found the derivative and got 3√x / 2 + 1/(x+3)^(3/2). I know for b you would sub in 1 and I got 1.625 but then c...is it not the same thing? what is the difference?
Click here to see answer by josgarithmetic(39618)

Question 1036460: The sum of Elliot�s age and twice Zane�s age is 44. The difference of twice Elliot�s age and Zane�s age is -2. What is Elliot�s age?
Click here to see answer by Aldorozos(172)

Question 1036470: Why is it important to know the domain and range?
Click here to see answer by Alan3354(69443)

Question 1036617: What is f(x+1)?
1) 7
2) 2a-5
3) 2a+5
4) a+5
The book says the answer is 3, but I need an explanation.
Click here to see answer by ikleyn(52794)

Question 1036752: 3/7-1/4y=1/2
Click here to see answer by Boreal(15235)

Question 1036740: Please help me solve this equation:
The function f is defined by f(x)=|x-2|-3. if f(a)=f(0) and a>0, what is the value of a?
Click here to see answer by rothauserc(4718)

Question 1036807: For the functions f and g, given that
f∘g = {(4,3), (�-1,9), (�-2,7)}
What is an example of sets of ordered
pairs for f and g that fits this
information?
Click here to see answer by Edwin McCravy(20056)

Question 1036834: The points (-1,14) and (9,14) are located on the same parabola.what is the equation for the axis of symmetry for this parabola?
Click here to see answer by Boreal(15235)

Question 1036786: The height of a projectile t seconds after being launched with an initial
velocity of 96 ft/sec from an initial height of 200 ft above the ground is given by the
following formula:
s(t) = −16t^2 + 96t + 200
(a) At what moment in time is the height of the projectile the greatest?
(b) At what moment in time does the projectile return to the ground?
(c) The slope of the line through points (t0, s(t0)) and (t1, s(t1)) is the average velocity
on the time interval [t0, t1]. What is the average velocity of the particle from the
moment it was launched to the moment when it reaches its greatest height?
Click here to see answer by Alan3354(69443)

Question 1036894: DID I ANSWER THIS RIGHT? I chose option D.
"Which of the following is the inverse of the function below?"
y = -2x - 1
A.) y = 2x + 1
B.) y = x/2 + �
C.) y = �x/2 + �
D.) y = -x/2 - �
Click here to see answer by Boreal(15235)

Question 1036959: Suppose f(x) = x
2 + 3x + 8. Evaluate and fully simplify f(x + h) − f(x)
________________
h

Click here to see answer by josgarithmetic(39618)

Question 1036877: Which of the following is the inverse of the function below?
Inverse & Function: http://postimg.org/image/dqcod3z8r/
A
B
C
D
?
Click here to see answer by Fombitz(32388)

Question 1037103: I've been given the following question and really need your help:
Given f(x)=√(1-x) and g(x)=x, which of the following is the domain of the quotient function ? Explain. 6._______
A. (-∞,0)
B. (-∞,0)∪(0,∞)
C. (-∞,0)∪(0,1)
D. (├ -∞,1] ┤
Thank you for any help!

Click here to see answer by ikleyn(52794)

Question 1037100: I'm having difficulty with the following problem:
Let f(x) = (x - 6)/(x^2- 1)
then I'm asked to:
a) calculate f(-2)
b) State the domain of the function f(x) = (x - 6)/(x^2- 1)
c) Find f(a+1) and simplify as much as possible.
I came up with -8/3 and (-infinity, infinity) and f(a+1)=a^2+ a+1^2- 1
I'm pretty sure I'm wrong on all of this, but I can't find clear answers. Please help.

Click here to see answer by josgarithmetic(39618)

Question 1037101: I've been given the following question and I'm completely lost:
f is a function that takes a real number x and performs these three steps in the order given:
(1) Take the absolute value.
(2) Subtract 4 from the result.
(3) Take the reciprocal of the result.
(That is, make the quantity the denominator of a fraction with numerator 1.)
(a) Find an expression for f (x). (no explanation required)

(b) State the domain of f. (no explanation required)
please help
Click here to see answer by ikleyn(52794)

Question 1037111: Hi there,
I took a crack at the below questions and this is what I came up with:
Let y = 4 - x2.
(a) Find the y-intercept(s) of the graph of the equation, if any exist. (work optional)
4
(b) Find the x-intercept(s) of the graph of the equation, if any exist. (work optional)
(-2, 2)

(c) Create a table of sample points on the graph of the equation (include at least six points), and use them to help create a graph of the equation. (You may use the grid shown below, hand-draw and scan, or you may use the free Desmos graphing calculator described under Course Resource to generate a graph, save as a jpg and attach.)

x y (x, y)
-2 0 (-2,0)
-1 3 (-1, 3)
0 4 (0,4)
1 3 (1, 3)
2 0 (2, 0)
3 -5 (3, -5)

(d) Is the graph symmetric with respect to the x-axis? _____ (yes). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.

(e) Is the graph symmetric with respect to the y-axis? _____ (yes). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.

(f) Is the graph symmetric with respect to the origin? _____ (yes). If no, state a point on the graph and state the appropriate reflection point which fails to be on the graph, as done in section 1.2 homework in the textbook.
Any help is very much appreciated! Thank you so much!

Click here to see answer by KMST(5328)

Question 1037114: Hi there,
I'm not exactly sure how to set up this problem. Any help is very much appreciated!
Let f(x) = 3x^2 + 7x � 5 and g(x) = 2 � x.
(a) Evaluate the function g � f for x = �1. That is, find (g � f)(�1).

(b) Evaluate the function fg for x = �1. That is, find (f g)( �1).

(c) Find the difference function (f � g)(x) and simplify the results.

Click here to see answer by ikleyn(52794)

Question 1037161: Hi there, I'm having trouble with this problem:
Let f(x) = 3x^2 + 7x � 5 and g(x) = 2 � x.
(a) Evaluate the function g � f for x = �1. That is, find (g � f)(�1).

(2 - x) - (3x^2 + 7x -5)
answer: -3 + 3x^2 + 6x

(b) Evaluate the function fg for x = �1. That is, find (f g)( �1).

(2 - x)(3x^2 + 7x -5)

answer: 2x^2 + 9x - 10

(c) Find the difference function (f � g)(x) and simplify the results.
answer: 3x^2 + 8x - 7

am I doing this correctly? I really appreciate any help!

Click here to see answer by Cromlix(4381)

Question 1037167: hi there, I really need help :(
My question is as follows:
sketch the graph of the given function, f(x) = x − 2 over 3. State the domain of the function, identify any intercepts and test for symmetry.
I really appreciate any help, thank you!

Click here to see answer by rothauserc(4718)

Question 1037255: Evaluate inverse function of f if f(x)=
Click here to see answer by Edwin McCravy(20056)

Question 1037353: please help mesolve this equation .if,in an arithmatic sequence,the 4th term is 5and the 7th term is9,what is d?

Click here to see answer by ikleyn(52794)

Question 1037620: Two functions f and g are such that f(x) = 1 + 2x and g(f(x)) = x + 3. What is the value of g(5)?
Click here to see answer by stanbon(75887)

Question 1037620: Two functions f and g are such that f(x) = 1 + 2x and g(f(x)) = x + 3. What is the value of g(5)?
Click here to see answer by josgarithmetic(39618)

Question 1037635: Suppose that the functions r and s
are defined for all real numbers x
as follows.
r(x)=2x+6
s(x)=3x
write the expression for (r+s)(x),(r-s)(x) and evaluate (r*s)(-1)
Click here to see answer by josgarithmetic(39618)

Question 1037706: At what value of x does 4x eventually exceed 7x2 + 8x + 2?
Click here to see answer by Alan3354(69443)

Question 1037706: At what value of x does 4x eventually exceed 7x2 + 8x + 2?
Click here to see answer by solver91311(24713)

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