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

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 Algebra: Rational Functions, analyzing and graphing Solvers Lessons Answers archive Quiz In Depth

 Question 83504: What is the GCF of the following expression: 16a4b2 + 20a2b2 - 4ab2 Click here to see answer by stanbon(57228)

 Question 83502: Factor the expression by taking out the GCF. 3x - 9x3 Click here to see answer by navytutor(7)

 Question 83501: What is the GCF for the polynomial -10x3y4 - 16x5y2? Click here to see answer by checkley75(3666)

 Question 83500: What is the GCF for the polynomial -10x3y4 - 16x5y2? Click here to see answer by stanbon(57228)

 Question 83566: The book asks for this group of problems to be tested to see if the function is one-to-one. The book gives an explanation of this test, but it is very short and of little help. Can you explain the testing process a little better? For instance, the example the book gives is f(x) = (sqrt x) + 1. It then assigns nonnegative real numbers a & b such that f(a) = f(b). In the end, a = b. How does this work with real problems like (3x+4)/5? Click here to see answer by nilan(15)

 Question 83499: What is the GCF for the polynomial 8x4y + 6x2y2 Click here to see answer by checkley75(3666)

 Question 83579: how do you solve 6x divided by x+4 plus 4 equals 2x+2 divided by x-1 Click here to see answer by ankor@dixie-net.com(15628)

 Question 83712: Factor the trinomial 9x2 - 18xy + 5y2 on your paper. Which of the following would be part of the factored answer? Click here to see answer by stanbon(57228)

 Question 83711: Factor the trinomial 4x2 + 24x + 11 on your paper. Which of the following would be part of the factored answer? Click here to see answer by stanbon(57228)
 Question 83711: Factor the trinomial 4x2 + 24x + 11 on your paper. Which of the following would be part of the factored answer? Click here to see answer by funmath(2925)

 Question 83862: Graph and answer the questions. f(x) = -x^2 + 4x - 1 What are the coordinates of the vertex? What is the domain? What is the range? Click here to see answer by jim_thompson5910(28493)

 Question 83942: Sketch the graphs, using the function and three points f(x)=x2+x-6 Click here to see answer by Nate(3500)

 Question 84122: How many ways can you arrange the letters in the word SMILE if the first letter must be an M? Repetition of letters is not allowed, since we only have these 5 letters to arrange. Click here to see answer by stanbon(57228)

 Question 84119: How many ways can you select pants, a shirt, and shoes if you have 5 pants, 7 shirts, and 3 pairs of shoes to choose from? Use a tree diagram to answer the question: How many ways can you select a lunch combo if you have 6 sandwich choices, 3 side choices, and 4 choices for drinks? A lunch combo consists of 1 sandwich, 1 side item, and 1 drink. Click here to see answer by stanbon(57228)

 Question 84121: How many different two-digit numbers can be formed using the digits 1, 3, 4, and 5. Repetition of digits is allowed. How many 7-digit phone numbers can be formed if the first digit cannot be 0 and repetition of digits is allowed? Click here to see answer by stanbon(57228)

 Question 84115: How many solutions are there to the quadratic equation 4x2 + 8x + 3 = 0? Click here to see answer by checkley75(3666)

 Question 84113: x2 + 3x - 13 = 0 9x2 - 16 = 0 x2-7x+12=0 3x2 - 2x + 7 = 0 Click here to see answer by checkley75(3666)

 Question 84118: When the discriminant is positive, or b2 - 4ac > 0, expect ___ root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. When the discriminant equals zero, or b2 - 4ac = 0, expect ___ root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. When the discriminant is negative, or b2 - 4ac < 0, expect ___ root(s). Use cardinal numbers (0,1,2,...) to fill in the blank. Click here to see answer by stanbon(57228)

 Question 84117: Find the discriminant for each of the following quadratic equations and use it to determine the number of roots or real solutions it has. 5. x2 - 2x + 8 = 0 6. -x2+5x+6= 0 7. x2 - 14x + 49 = 0 Click here to see answer by venugopalramana(3286)

 Question 84186: Solve each rational equation and simplify. I would like to check my solutions. Problem 1. x + 5 = 6 / x Problem 2. 13 / y - 1 (-3) = 1 / y - 1 Click here to see answer by checkley75(3666)

 Question 77847: Science and medicine. A passenger train can travel 325 mi in the same time a freight train takes to travel 200 mi. If the speed of the passenger train is 25 mi/h faster than the speed of the freight train, find the speed of each. thanks Click here to see answer by vertciel(183)

 Question 84457: Find all the discontinuities for the function below. Label each as a vertical asymptote or removable discontinuity. y = x - 6/ x^2 - 6x Click here to see answer by venugopalramana(3286)

 Question 84456: Find all the discontinuities for the function below. Label each as a vertical asymptote or removable discontinuity. y = 4x + 28/ x^2 + 6x - 7 Click here to see answer by venugopalramana(3286)

 Question 84550: what rational numbers are roots of the equation (X2-7)(X2-9)=0 Click here to see answer by funmath(2925)

 Question 84674: given: f(x)= x^2+2 and g(x)= 3x+1 a) find the composition (f of g)(x) b) find the inverse function g^-1(x) Click here to see answer by dolly(163)

 Question 84921: I have tried to make sense of this one and it bugs me and is even harder with no graphing calculator.:-( Page 795: Problem # 56 solve the inequality and graph the solution set on a real number line. A model rocket is launched from ground level. The function: S(t) = -16t^2 +48t Models the rocket’s height above the ground, s(t) in feet, t seconds after it was launched. During which period will the rocket’s height exceed 32 feet? Click here to see answer by stanbon(57228)

 Question 85000: Given f(x) = 2x^2 - 3x + 4, find the following: f(4) f(-3) f(0) Click here to see answer by tutorcecilia(2152)

 Question 85785: A. Is the following binomial a difference of squares? 9a^2 – 8b^2 B. If one-half a number is subtracted from five-sixths of the number, the difference is 6. Find the number Click here to see answer by ankor@dixie-net.com(15628)

 Question 85816: r to the second power, minus 5r+6 over r to the second power -4= Click here to see answer by Earlsdon(6287)

 Question 86383: 2/sqrt[3] + sqrt[2] Can you help me rationalize the denominator? I really apprecuate your help. It would help so much if you could show me how you do this. Click here to see answer by stanbon(57228)
 Question 86383: 2/sqrt[3] + sqrt[2] Can you help me rationalize the denominator? I really apprecuate your help. It would help so much if you could show me how you do this. Click here to see answer by Edwin McCravy(8880)

 Question 86648: for the following function, one zero is given. find the other zeros. P(x)=x^3-6x^2+3x+10; -1 Click here to see answer by Earlsdon(6287)

 Question 86809: x^3- 3x^2-4x+12=0 i have to solve for x Click here to see answer by checkley75(3666)

 Question 86978: This question is really bothering me. Please help. Express f(x) = x2 + │x+3│ - 1 without the absolute values and hand-graph. Hint: │x│= x if x ≥ 0 or = –x if x < 0 Click here to see answer by stanbon(57228)

 Question 86977: Let f(x) be any function and O(x) = [f(x) – f(-x)]/2 . Show that O(x) is odd. This question is really giving me a hard time. I would love it if someone could please help me. Click here to see answer by stanbon(57228)

 Question 87129: Ok the problem is functions where the instructions say find f(-3), f(0), f(5) where f(a)=3/4a -1. Im terrible with fractions. I need help in how to understand the solutions which in the back of the book have: -13/4,-1,11/4. i get the answer for f(0) but what about the others. help please. im terrible with fractions. Click here to see answer by longjonsilver(2297)

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