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

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Question 998583: graph the function the following equation by finding the vertex ,intercepts and axis of symmetry:-x2-8x-15
Click here to see answer by josgarithmetic(39613)

Question 998582: graph the function f(x)=|x-5|+3
Click here to see answer by ikleyn(52747)

Question 998595: I need help solving this problem:
f(x)= -3/x+8

Click here to see answer by ikleyn(52747)

Question 998621: Use the following functions. f(x)=x , g(x)=x-3, h(x)=x^2-9 , k(x)=2x.
Find each function. A). (g+k)(x) ,
B). (k-f)(x) ,
C). (k/f)(x) ,
D. (hk)(x) .
Click here to see answer by MathLover1(20849)

Question 998553: For f(x)= 1/x^2-3 Find:
a. f(3)
b. f(2+h)
Click here to see answer by Alan3354(69443)

Question 998708: Which is the inverse of f(x)=(x+7)^2/6?
A. y=6(x+7)^-2
B. y=-7�6√x
C. y=-(x+7)^2/6
D. y=-7�√6x
http://prntscr.com/8uvqpv
Click here to see answer by josgarithmetic(39613)

Question 998711: Which is the inverse of f(x)=x-3?
A. y=1/x-3?
B. y=-x+3?
C. y=x+3?

thank you.
Click here to see answer by josgarithmetic(39613)

Question 998713: Given P(x)=-5x^4-3x^3+11x^2+16x-9, which of the following is true?
A. P(x) is odd, and as x > + ∞, P(x) > - ∞.
B. P(x) is odd, and as x > + ∞, P(x) > + ∞.
C. P(x) is even, and as x > + ∞, P(x) > - ∞.
D. P(x) is even, and as x > + ∞, P(x) > + ∞.
Thanks
Click here to see answer by ikleyn(52747)

Question 998705: Suppose f(x)=(x/8)-3 and g(x)=x^3. Find (f o g)^-1(x)
Click here to see answer by Edwin McCravy(20054)

Question 998957: http://prntscr.com/8vcrv6
Link to question help please , thanks.

Click here to see answer by KMST(5328)

Question 998956: Evaluate
link to problem ; http://prntscr.com/8vcr4j
copy and paste please,
A). f(11)=1
B). f(11)=6
C). f(11)=3
D). f(11)=9
thank you

Click here to see answer by fcabanski(1391)

Question 998938: Evaluate
f(x)={2x if x ≤ 0
{x-2 if x > 0
at x-0.
A). f(0)=-2
B). f(0)=0
thanks!
here is a picture of it, if how i typed it doesn't come out right.
Copy and paste link : http://prntscr.com/8vc6ky
Click here to see answer by fcabanski(1391)

Question 999022: Complete table for 2x+7y=5
Click here to see answer by Edwin McCravy(20054)

Question 998597: what is the domain of the real-valued function f(x)?
Link for the problem http://prntscr.com/8ul55h

Click here to see answer by Fombitz(32388)

Question 998618: Use the following functions f(x)=x , g(x)=x-3, h(x)=x^2-9 , k(x)=2x.
Find each value .
A). g(g(-1))
B. f(g(2))
C. g(k(2))
D. h(g(3))

Click here to see answer by Fombitz(32388)

Question 999048: Let f(x) =x^3+2x/5x+7, find f'(x)
Click here to see answer by fractalier(6550)

Question 999123: Each month, Jason wants to save money for a mini IPAD. The mini IPAD costs $300. Jason has $120 and can save $40 a month. The function for this situation can be represented as: S(m) = 40m + 120 where m represents the number of months and S (m) represents the amount of money saved after those months.
f(1)= $160 f(2)= $200 f(3)= $240 f(4)=$280 f(5) = $320
Therefore, after 5 months of saving, Jason has enough to buy the mini IPAD. So, what is the domain and range of this function?
Click here to see answer by stanbon(75887)

Question 999117: The function f(x) represents the total bill from a rental store that charges $10 to rent a power tool plus an additional $2 an hour. A second rental store uses the function g(x)=15+1.5x to represent the total bill for a similar power tool.
Which of the following statements is true about the functions f(x) and g(x)?
a. The function f(x) has a greater rate of change than the function g(x).
b. The function g(x) has a greater rate of change than the function f(x).
c. The rates of change for both f(x) and g(x) are equal.
d. The rates of change cannot be determined.
Click here to see answer by stanbon(75887)

Question 999115: A candle burns at a rate of 1 inch per hour. The original height of the candle is 12 inches. The function of the candle burning can be represented by f(x)=-x+12. Find x when f(x)=8.
Click here to see answer by Alan3354(69443)

Question 999299: Find vertex,axis of symmetry, y-intercept and x-intercepts
(-1/2)(y+4)=(x-3)^2
Click here to see answer by Fombitz(32388)

Question 999407: Trying to find the intervals where this function increases and decreases but running into some problems.
So I know to find the critical values first:
f(x) = x^4 + 2x^3 +1
f'(x) = 4x^3 +6x^2
f'(x) = 2x^2(2x+3)
x = 0 and x = -3/2 are the critical values.
Now, if I understand correctly I use the first derivative test to determine in between these two critical values where it's increasing/decreasing.
Therefore, I make a number line and I plug in values around them into the derivative.
<----(-2)----(-3/2)----(-1)----(0)----(1)---->
f'(-2) = 4(-2)^3 + 6(-2)^2 = -8 therefore (-) on the left of (-3/2)
f'(-1) = 4(-1)^3 + 6(-1)^2 = 2 therefore (+) on the right side (-3/2) and left of (0)
f'(1) = 4(1)^3 + 6(1) = 10 therefore (+) on the right of (0)
bit confused on why on the left of (0) there would be another (+) I thought it worked by -,+,-,+ what do I get when I have two (+)'s or two (-)'s in a row like this?
All I can deduce now is that I have a minimum between -2 and -3/2.
Maybe I am getting things confused here with other methods.
But since I have proven I have a (-) the left of (-3/2) does that imply that the function is decreasing from (-inf,-3/2) then increasing from (-3/2, +inf) and thus increasing (0,inf)
Feel like I am really misunderstanding something here
Please clarify
Thank yu

Click here to see answer by jim_thompson5910(35256)

Question 999434: How do I solve the following:
f(x) = x^2 - 3
f(5)

Click here to see answer by ikleyn(52747)

Question 999461: ok, so i'm in algebra one, and i have a test tommorow on our unit. one thing I don't get is domain and range. it shows an oval, and three numbers inside. i get the first and last one, but not the middle one. I don't know how to make a piecewise function with the {{}} thing so i'll put it as 2 layers. the piecewise function that i need help on is:
f(x)=3x+11 -5<=x<=-2
-x/2+5 -2 sorry for bad grammar i rushed through this! :)
Click here to see answer by stanbon(75887)

Question 999529: Suppose you are given a radioactive substance. After 30 days there is 1/10 of the original amount remaining. What is the half-life of the substance?

I am confused here on what formula I should use and which is most efficient.
R(t) = re^(-kt)
where,
R(t) = the decay rate at time t
r = initial decay rate (at t=0)
t = time
k = the decay constant
Or
A = a(1/2)^(t/h)
Where,
A = final amount
a = initial amount
1/2 = split-factor
t = time
h = half-life
Please explain how to solve this problem using the one which you think is the most efficient.
Thank you
Click here to see answer by josgarithmetic(39613)

Question 999522: Find the area of the largest rectangle that has two sides on the positive x-axis and the positive y-axis one vertex at the origin and one vertex on the curve y = e^(-x)
Explain how you know the value you found is the maximum area.
Thank you
Click here to see answer by Theo(13342)

Question 999524: a). Suppose a population is growing exponentially with p(0) = 1,000.000 and P(2) = 2,000.000. Find p(3) = ?
b). Let f be a continuous on [0,2] and differentiable on (0,2). What does the Mean value Theorem state about f?
Thank you
Click here to see answer by Fombitz(32388)

Question 999419: Find an equation of a straight line that passes through point points (3,5) and is perpendicular to line which passes through points (-1,-3) and (-2,-5)
Click here to see answer by Fombitz(32388)

Question 999564:
Click here to see answer by Amayaroka1237(3)

Question 999602: Please check my work for max/min problem.
Find the max/min of:
f(x) = 2x^3 - 3x^2 + 6 of f on [-1,1]
f'(x) = 6x^2 - 6x
f'(x) = 6x(x-1)
therefore, x = 0 & x = 1 and including the boundary x = -1
testing...
f"(x) = 12x - 6
f"(0) = 12(0) - 6 = -6 < 0, MAX value occurs at x = 0
f'(1) = 12(1) - 6 = +6 > 0, MIN value occurs at x = 1
f"(-1) = 12(-1) - 6 = -18 < 0, MAX value occuras at x = -1
This confuses me because now I have one MIN value that occurs at x = 1, but this isn't actually the value of the MIN just where it occurs right?
And then I have two MAX's which one is the real max? because I think I am only dealing with rel max/min so I don't think two would make sense.
Plese explain
Thank you

Click here to see answer by Fombitz(32388)

Question 999598: I was able to solve this function {h(t)=|t+2|+3;Find h(6)
6+2+3= 11 so h(t)=11
I don't understand how to solve this one where the (n) is included
w(n)=4n+-2; find w(3n)
Click here to see answer by fractalier(6550)

Question 999660: For f(x)= 1/x^2-3 Find:
a. f(3)
b. f(2+h)
(The denominator is x^2-3 not just x^2)
Click here to see answer by Fombitz(32388)

Question 999753: f(x) = x√(1-x^2)
f'(x) = (1-2x^2)/√(1-x^2)
f"(x) = (2x^3-3x)/((1-x^2)^(3/2))
now to find the inflection pts I need to set the 2nd derivative to zero and find what x equals. However, since it's a rational function I dismiss the denominator, right? because it cannot be divided by zero.
If so I get:
2x^3-3x = 0
2x^3 = 3x
x^2 = 3x
x = � √(3/2)
technically isn't these two the inflection points?
When I plug it into my program it tells me this is wrong.
Any ideas?
Thanks
Click here to see answer by stanbon(75887)

Question 999894: f(x)= 〖2x〗^2-16x+30 ,
g(x)= 〖x(x-3)〗^2 〖(x+1)〗^4
Find the zeros of g(x)and f(x)

Click here to see answer by Boreal(15235)

Question 999910: Please check my work
The problem gives me the function:
f(x) = ((2x-1)^2)/(2x^2)
I must find the intervals where f is increasing and decreasing.
And
I must find the intervals where the graph is concave down and concave up.
And
Identify all relative extreme values of f.
Here's what I did:
f(x) = ((2x-1)^2)/(2x^2)
f'(x) = (2x-1)/(x^3)
f"(x) = (3-4x)/(x^4)
These were given already by the problem. I am worried that wouldn't be able to figure out these derivatives they seem tricky to get them simplified into those forms.
To find where f(x) is incr/decr I look at the 1st derivative and set equal to zero and get: x = 1/2 I pretty sure this exists because it's in the NUMERATOR. However, the part which I am really confused by is what to do about the denominator. Since it can never be zero how can it ever be anything. Someone told me that if it's odd then we "consider it" if it's even we "dismiss it" if this is true, why is it?
Provided it is. x =1/2 and x = 0 for critical values.
testing pts....
<--(-1)--[0]--(+1/4)--[+1/2]--(+1)-->
f'(-1) = ((2)(-1)-1)/((-1)^3) = +
f'(1/4) = (2(1/4)-1)/((1/4)^3) = -
f'(1) = (2-1)/(1^3) = +
Therefore,
is incr int(-inf,0)U(1/2,1)
is decr int(0,1/2)
For testing concave up/down intervals
I found the inflection pt from setting the 2nd derivative to zero and testing points around it.
f"(x) = 3-4x = 0
//now in this case, there was a x^4 in the denominator, but since it was even we disregard it?
x = -3/4
<--(-1)--[-3/4]--(0)-->
f"(0) = DNE because of the zeros
f"(-1) = (3-4(-1))/((-1)^4) = +
Therfore,
It is concave up (-inf,-3/4)
And concave down DNE
Please correct any errors I have made.
Thank you
Click here to see answer by Fombitz(32388)

Question 999972: What is the domain and range of y=-5x+0

Click here to see answer by MathLover1(20849)

Question 1000007: Let
g(x)equals=-x^2+3x+4.
Find g(p).
Click here to see answer by MathLover1(20849)

Question 1000034: How to find the unknown coefficients when the vertex is given: (3,-4)
y=x^2 + bx + c
Click here to see answer by jim_thompson5910(35256)

Question 1000038: If f(x) = 4x2 - 3x + 2, evaluate f(-1).
State the domain of the function f(x) = (x+3)/(x-1).
Write the equation of the line that passes through the points (1, 1) and (2, 4). Write your answer in slope-intercept form.
Write the equation of the line with a slope of 2/3 and y-intercept of 1. Write your answer in slope-intercept form.
Solve the equation: (4x+1)(2x-7) =0.

Click here to see answer by josgarithmetic(39613)

Question 999993: Say that f(x) = 2x - x. What would be the result of f(5)

Click here to see answer by fcabanski(1391)

Question 1000047: find the exact area of a triangle whose side lengths are the roots of
x^3-18x+105x-200
Click here to see answer by fractalier(6550)

Question 1000126: If f(x) = 4x + 3, evaluate f(x+h).
If g(x) = x�, evaluate g(x+h).
If f(x) = -x + 1, evaluate f(x+h).
If f(x) = -x + 1, evaluate f(x-h).
Use the quadratic formula to solve the equation: x� - x - 1 = 0.
Click here to see answer by stanbon(75887)

Question 1000167: Evaluate each piecewise function for x=-3 and x=4.
A).
f(x)=
{10 if x < 4
{-1 if x ≥ 4
B). g(x)=
{3x-1 if x < 0
{2x^2 if 0 ≤ x < 4
{1-x if 4 ≤ x
thanks!

Click here to see answer by stanbon(75887)

Question 1000169: If f(x) = 4x + 3, evaluate f(x+h).
If g(x) = x�, evaluate g(x+h).
If f(x) = -x + 1, evaluate f(x+h).
If f(x) = -x + 1, evaluate f(x-h).
Use the quadratic formula to solve the equation: x� - x - 1 = 0.
Click here to see answer by Boreal(15235)

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