Questions on Algebra: Rational Functions, analyzing and graphing answered by real tutors!

Tutors Answer Your Questions about Rational-functions (FREE)

Question 283217: Find the following. assume that variables can represent any real number
square root(a+4)^2
Click here to see answer by richwmiller(9143)

Question 283243: if f(x)=x^2 - 7x, find f(a), f(a - 3), and f(a h)?
Click here to see answer by richwmiller(9143)

Question 283467: find the equation of the vertical line that passes through(3/4, -6)
Click here to see answer by richwmiller(9143)

Question 283528: How would i find the maximum number of turns in an equation like this: f(x)= 3X+2?
Click here to see answer by richwmiller(9143)

Question 283682: Use the Binomial Theorem to expand each binomial and express the result in simplified form.
(3x + y)^3
Click here to see answer by jim_thompson5910(28598)

Question 283760: graph x^2-8x+2
Click here to see answer by Theo(3464)

Question 283733: (4/n+7)-(7/n-2)
Click here to see answer by dabanfield(803)

Question 283889: This is what I have so far - K=kmv^2
4500=k(90)(20)^2=36000/4500=8. I'm not sure if this means 1/8 therefore making K=1/8(90)(32)^2=92160/8(?) = 11520
K=11520 Joules ??? The actual problem is below.Any help is so appreciated. Kevin

Problem: The kinetic Energy (K) of a moving object varies jointly with its mass (m) and the square of its
velocity (v). If an object weighing 90 kilograms and moving with a velocity of 20 meters per second has a
kinetic energy of 4500 Joules, find its kinetic energy when the velocity is 32 meters per second.
Click here to see answer by Alan3354(30993)

Question 283746: f(x)=2x^2-32
_______
3x^2 +3x-60
Click here to see answer by jim_thompson5910(28598)

Question 284561: What is the answer to the rational expression, (x-5)(x+4)/(x+5)(x-5)?
Click here to see answer by richwmiller(9143)

Question 284693: 4/x+5/2=-11/x
Click here to see answer by mananth(12270)

Question 284624: I don't know how to do f(g(x)) expressions can you help me? these are the formulas for f and g. f(x)=2^2-x, g(x)=x-4. The problem is (fg)(x). Thank you for helping me understand this topic.
Click here to see answer by nyc_function(2733)

Question 284804: Please help. I try to work these problems on my own but it confuses me.
The function y(x) = 48.94 lnx/4.5 can be used to estimate the number of years y(x) after 1980 required for a certain country,s population to reach x million people. In what year will the country's population reach 11 million?
Click here to see answer by stanbon(57399)

Question 284843: Please help, I don't want to fail this course.
log(x + 4) - log(x - 2) = log3
Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists state this.
Click here to see answer by Alan3354(30993)

Question 284872: This is over my head. Could you please help me? I am desperate.
logn 14.2
Find the logarithm using the change-of-base formula, round to the nearest ten-thousandth.
Click here to see answer by Alan3354(30993)

Question 284836: One root of x^4-x^3-7x^2+x+6 is x=-1 What is another root?
-1] 1 -1 -7 1 6

-1 +2 +5 -6
__________________
1 -2 -5 6 0
x^3-2x^2-5x+6
I am lost from this point, do I factor by using grouping then find the additional roots?
Thank you for your help I appreciate it very much.
Tina

Click here to see answer by Fombitz(13828)

Question 285002: How do you solve this promblem 5divided by x minus 5. plus x divided by 2x minus 10?

Click here to see answer by richwmiller(9143)

Question 285204: Solve. Where appropriate, include approximations to four decimal places.
An investment with interest compounded continuously doubled itself in 16 yr. What is the interest rate?
Can someone please help me?
Click here to see answer by rfer(12670)

Question 285432: Solve. Where appropriate, include approximations to the nearest thousandth. If no solution exists, state this.
log9x = -3
Can someone please help me step by step so I can understand how to get the answer?
Click here to see answer by user_dude2008(1861)

Question 285589: Write a function that models the variation.
{x=3 & y=12} if z=2
z varies directly with y and inversely with x.
I tried this problem, and came up with the equation,
z=(1/18y)/x
Is this correct? If not, how do I solve this problem?
Thanks.
Click here to see answer by Alan3354(30993)

Question 285613: 1 + 2/x = 3/ x^2
x/ x-1 + x = 4x - 3/ x - 1
Please help....I am so lost. I have no idea even where to start.
Click here to see answer by Alan3354(30993)

Question 285596: Write an equation for the translation of y=2/x with the given asymptotes.
x=1 y=1
and
x = 5 y= 0.5
Help?
Click here to see answer by richwmiller(9143)

Question 285476: f(x)=x+1; g(x)=2x
find (f o g)(x)
Click here to see answer by dabanfield(803)

Question 285592: I think I chose the right category.. not sure though. I need help with this question:
One measure of form for a runner is stride rate, defined as the number of steps per second. A runner is considered to be efficient if the stride rate is close to optimum. The stride rate is related to speed; the greater the speed, the greater the stride rate.
In a study of 21 top female runners, researchers measured the stride rate for different speeds. The following table gives the average stride rate of these women versus the speed.
Speed:

15.86

16.88

17.50

18.62

19.97

21.06

22.11
Stride Rate:

3.05

3.12

3.17

3.25

3.36

3.46

3.55
(the speed and stride rate go together so you can graph them, so like number 1 in the speed and number 1 in the stride rate etc..)
a. Using Graphit, TI83/84 or EXCEL, plot the data on a scatter-plot. Be sure to include a title, scale and a label for each axis.
b. Identify the function that you feel best fits the data. Explain how you decided on the function to use.
c. Make a prediction of the stride rate if the speed is 19 feet per second. Show, or explain how you determined your answer.
Click here to see answer by stanbon(57399)

Question 285880: Rationalizing the Denominator
Numerator is 6
Denominator is 2 times the radical expression square root of five plus 2.
I can't figure out how to rationalize this denominator because of the extra "+2" at the end of the denominator. If you could please explain what I need to do and WHY I need to do it, that would be awesome! I can usually figure these things out once I know why I need to do a particular step.
My book says the answer is
Numerator is 3 times the radical expression square root of 5-3
Denominator is 4.
I know that I should multiply both the numerator and the denominator by the radical, but I've come up with a million wrong answers and still can't figure out where the book finds a way to put a 3 in the numerator.
Do I multiply by 2 times the radical MINUS 2 over itself?
I just can't figure out where this silly 3 comes into play.
Any help with this question is greatly appreciated, because I know it will help with the rest of my assignment as well as on my test!
Thanks in advance.
Click here to see answer by ankor@dixie-net.com(15661)

Question 286167: find all numbers for which the rational expressions is undefined r^3-4r0ver r^2-16 the numbers for which the rational expression is undefined are

Click here to see answer by richwmiller(9143)

Question 286230: For the function f(p) an input of 2 yields an output value of 3. What value of p would you use to have f(9p) = 3?
I'm not sure what to do here. If I was just solving for p in the second function, I would just say it was 1/3, but I don't know what the first function means in reference to the whole problem. Any help would be really appreciated.
Click here to see answer by richwmiller(9143)

Question 286257: what is the index of this equation:
y(x)=3x^20-6x^14+x^12-x+8
Click here to see answer by Alan3354(30993)

Question 286271: solve:
x^4-4x^2-12=0
Click here to see answer by richwmiller(9143)

Question 286273: If g(x)=3x+8, solve g[g(x)]=g(x) for x.
Click here to see answer by stanbon(57399)

Question 286276: Find all the zeros of the function:
p(x)=X^3-2x^2+9x-18
Click here to see answer by stanbon(57399)

Question 285387: Can someone please, please help me with this problem?
Evaluate the exponential equation for three positive values of x, three negative values of x, and at x=0. Transform the second expression into the equivalent logarithmic equation; and evaluate the logarithmic equation for three values of x that are greater than 1, three values of x that are between 0 and 1, and at x=1. Show your work. Use the resulting ordered pairs to plot the graph of each function.
y=2x, x=2y
Click here to see answer by richwmiller(9143)

Question 286441: y is directly proportional to the square of x and inversely proportional to the cube of w, y=18 when x=9 and w=3. Find y when x=3 and w=5
Click here to see answer by jim_thompson5910(28598)

Question 286453: For the function f(x)=x squared + 2/x-1 How do I check for symmetry and find the y-intercept? I think I was able to find the x-intercept by plugging in the function equation x=0.
Click here to see answer by jim_thompson5910(28598)

Question 286481: (x/3)-(5/x-2)
Click here to see answer by stanbon(57399)

Question 286652: how do you multiply these rationals?
5x^3y/x^2y^2 * y^3/15 x^2
i got 5x^3y^4/x^2y^2 * 15x^2 but i dont know if that is right
Click here to see answer by richwmiller(9143)

Question 286660: how do you multiply these rationals?
x(x-3)/(x-2) * (x+3)(x-2)/x
i got x^3(18)/(x-2) is that correct?
Click here to see answer by Alan3354(30993)

Question 286660: how do you multiply these rationals?
x(x-3)/(x-2) * (x+3)(x-2)/x
i got x^3(18)/(x-2) is that correct?
Click here to see answer by stanbon(57399)

Question 286690: write the rational expression in lowest terms:
4x-16/16-x^2
Click here to see answer by richwmiller(9143)

Question 286758: Let f(x)= 2x^3-6x^2+2x+11 / x^2-4x+5. This is a function of x
A) Find the natural domain of f
B)Find the standard form of f
C) Find any straight line asymptotes of the graph y=f(x)
Please show working..
Thanks!
Click here to see answer by stanbon(57399)

Question 286840: For the functions and given by:
and
find (FºG)(x)
I solved the question, but I need some help on how to simplify it
my answer was
Click here to see answer by richwmiller(9143)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055