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

Tutors Answer Your Questions about Rational-functions (FREE)

Question 87151: Which, if any, of the following equations is a function of x?

A. y=2x - 10
B. (y+1)squared + (x+4)squared = 36
C. absolute value of y = 3x
D. None of these equations represents a function
Click here to see answer by tutorcecilia(2152)

Question 87163: sketch a graph of the fuction.
1. Y=1/x-3
2. Y=(1/x+1)+1
Click here to see answer by tutorcecilia(2152)

Question 87219: Determine any (global) maxima or minima of the function g(x)=x^2-x-20.
Click here to see answer by Nate(3500)

Question 87218: For the function f(x)= -3x^2 + x- 11, determine the difference quotient
f(a+h) - f(a)/h where h is not equal to 0. Simplify your result as much as possible.
Click here to see answer by Nate(3500)

Question 87220: Determine, approximately using a graph, the intervals on which the function
f(x)=x^3 + 3x^2-7x-1 is increasing and decreasing.
Click here to see answer by Nate(3500)

Question 87217: Graph the functions L(x)= -3x+17 and Q(x)=2x^2+7x-22 on the same set of axes.
Click here to see answer by Nate(3500)

Question 87366: Explain the difference between simplifying the expression 4/x + 1/2 - 1/3
and solving the equation 4/x + 1/2 = 1/3.
Click here to see answer by longjonsilver(2297)

Question 87478: for the function y=1/x-2
Give the values of x = -1, 0, 1, 2, 3, 4
Using the points, draw a curve.

Click here to see answer by rapaljer(4667)

Question 87508: I could really use some help on this one. For the function f(x) = x² - 3x + 4 construct and simplify the difference quotient f(x) = [f(x+h) – f(x)]/h

Click here to see answer by rapaljer(4667)

Question 87559: The book is Algebra, 3/e, by K. Elayn Martin-Gay!

Determine whether each of the following is an equation or an expression. If is an Equation, solve it for its variable. If its an expression, perform the indicated operation.
1. 1 2
- + -
x 3
I know the we need to find a LCD but i not sure wich one would be i got x(3)for my LCD????
and for my answer i got 3+2x over 3x
...but i not sure if thats correct...Please Help...if you can help me please explain me why, and how can i get it..so i can understand...Thanks
Click here to see answer by checkley75(3666)

Question 87625: Given the functions f(x)=sqrt-3x+15 and g(x)=5/x, determine g * f(x) and find its domain.
*please note that the question has a small o where I have placed an * symbol. I am not sure what that means.
Please someone help me.
Click here to see answer by Earlsdon(6287)

Question 87738: Please please help. I have asked this question three times cansomeone help me.\
Write a rational expression, in its simpliest form, that represents the sum of the reciprocals of the squares of the consecutive even intergers n-2, n, and n+2. That is the expression should be in terms of the interger variable n.
Click here to see answer by ankor@dixie-net.com(15628)

Question 87889: f(x)=4x2-3x+2
f(-30)= NEED CALCULATIONS STEP BY STEP
f=(30)= NEED CALCULATIONS STEP BY STEP
Very confused - need help - please!!!
Click here to see answer by jim_thompson5910(28493)

Question 87885: x² - y + 4 = 3x
Need to solve for y in terms of x - line by
line and tell if a function or not -why or
why not
Thanks
Click here to see answer by Edwin McCravy(8880)

Question 87881: x2-64
-----
x2-8x+16
Click here to see answer by checkley75(3666)

Question 88132: Word problem: A typist has completed 1/6 of a paper. 6 hours later, the paper is 3/4 complete. Calculate the typing rate.
I want to find out how much of the paper is completed each hour until it is 3/4 complete, when 1/6 is already done.
I've tried to graph this and I've tried to plug it in to pythagorean theorem and have tried the distance formula.
I've tried f(x)=1/6x=6 where x=3/4. But that's not right. I've tried my dad, and he can't figure it out.

Click here to see answer by tutor_paul(490)

Question 88243: find two numbers of which the sum is 11 and the difference is 5.
Click here to see answer by jim_thompson5910(28493)

Question 88370: how can i find the domain of the rational function f(x)= (x - 1)/(x - 5)(x + 7)
Click here to see answer by Nate(3500)

Question 88369: How do i simplify the rational expression x^2+7x+12 / x^2+9x+20
Click here to see answer by Nate(3500)

Question 88355: Please
Thank you!!
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 88354: Please solve this formula for the indicated variable:
I=E/R+r for R
Thank you!!1
Click here to see answer by rapaljer(4667)

Question 88443: At the high school band's annual spaghetti dinner, the members served 210 dinners and collected $935. The band leader did not designate which ticket was an adult or child dinner. You need to know that to prepare the correct amount of food and for future planning. Each adult dinner cost $6 and each child's dinner cost $3.50.
Let a = number of adult dinners
Let c = number of child dinners

1. Write two equations to represent the total amount raised from the dinner and the total.

You need to have 2 equations -- one for the total number of dinners and one for the total amount of money made.

--------------------------------------------------------------------------------
2. Use substitution to solve the above system of equations. How many adult dinners were sold and how many child dinners were sold?
Show all your work to receive full credit for this problem.

Substitution means to solve one equation for one variable and substitute that into the other equation. You will then have only one variable in your equation.

Click here to see answer by checkley75(3666)

Question 88444: 6. The sum of two numbers is 28. The larger number, y, is 4 more than the smaller number, x. Write two equations for this system and solve to find x and y.
Give your answer as an ordered pair without parentheses or spaces, as in x,y.

Click here to see answer by checkley75(3666)

Question 88442: Show all your work to receive full credit for this problem.
Use the Substitution method to solve the system of equations. Give your answer as an ordered pair (x,y).

x + y = -5
x - y = 3

Click here to see answer by jim_thompson5910(28493)

Question 88445: 1. Six pears and three apples cost $3.90. Two pears and five apples cost $3.30. How much does one pear cost? Hint: You have two unknowns (variables), so you need two equations. Write one equation for each situation and solve the system of equations.
Let p = the cost of one pear
Let a = the cost of one apple
a. Write a system of equations that can be used to determine the cost of pears and apples.
b. Determine the cost of one pear and one apple. Use mathematics to explain how you determined your answer.

2. There were 1500 people at a high school football game. Student tickets were $2.00 and adult tickets were $3.50. The total receipts for the game were $3825. How many students bought tickets?

Let a = the number of adult tickets purchased.
Let s = the number of student tickets purchased.
a. Write a system of equations that can be used to determine the number of adult and student tickets purchased.
b. Determine the number of adults tickets sold and the number of student tickets sold. Use mathematics to explain how you determined your answer.

3. An airplane flew 4 hours with a 25 mph tail wind. The return trip against the same wind took 5 hours. Find the speed of the airplane in still air. This similar to the current problem as you have to consider the 25 mph tailwind and headwind.
Let r = the rate or speed of the airplane in still air.
Let d = the distance
a. Write a system of equations for the airplane. One equation will be for the outbound trip with tailwind of 25 mph. The second equation will be for the return trip with headwind of 25 mph.
b. Solve the system of equations for the speed of the airplane in still air.

4. Your family likes to go to baseball games. At one game your family bought 5 soft drinks and 5 hot dogs for $22.25. At the next game your family attended they bought 4 soft drinks and 3 hot dogs for $14.50. What is the cost of one soft drink and one hot dog?
Let s = the cost of one soft drink
Let h = the cost of one hot dog
a. Write a system of equations modeling the situation described above.
b. Solve the system for the cost of one soft drink + one hot dog. (You will have to add your solutions together for this one.)

5. Suppose you just have just enough dimes and quarters to pay for a loaf of bread and quart of milk, which cost $3.45. You have a total of 15 dimes and quarters.
Let d = the number of dimes you have.
Let q = the number of quarters you have.
a. Write a system of equations that models the information given above.
b. Solve the system for the number of dimes and quarters you have. You may want to solve this by graphing.

Click here to see answer by checkley75(3666)

Question 88204: Please help me with this question: Find the LCD for this rational expression and convert the rational expression int an equivalent rational expression with the LCD as the denominator:
__4___ ___5x___
x-y’ 2y-2x

Click here to see answer by checkley75(3666)

Question 88626: Solve ln(5-x) = 12.
Click here to see answer by ankor@dixie-net.com(15628)

Question 88626: Solve ln(5-x) = 12.
Click here to see answer by bucky(2189)

Question 88766: How do I enter this problem to work it?
Use formula x=-b/2a to find the coordinates of the vertex for the parabola defined by the quadratic function f(x)=2x^2+4x-15. Substitute this value into the f(x) to find the y coordinate of the vertex. Plot two points to the left and right of the vertex. Do the graph of the parabola. HELP!!!
Click here to see answer by Earlsdon(6287)

Question 88807: Here is the problem:
Determine without graphing, whether the given quadratic function has a minimum value or maximum value. Then find the x and y coordinates of the minimum or the max point f(x)=X^2-2x-8
Here is what I have done
x=- b/2a
x=- -2/2(1)
x=2/2(1)
x=2/x
x=1
f(1)=(1)^2-2(1)-8
f(1)=(1)-2(1)-8
f(1)=(1)-2-8
f(1)=-1-9
f(1)=-9
Is this right?

Click here to see answer by bucky(2189)

Question 88886: i have this 1 more question
for all x not equal to -4, wich of the following is equivalent to x^2 +12x+32/x+4
and the options are:
a)x+3
b)x+8
c)x+11
d)x+16
how do i solve it??
Click here to see answer by stanbon(57228)

Question 88988: Find the equation of the line with x-intercept 5 and y-intercept 8.
Show all work.
I got y = -(8/5)x + 8 Is that right?
Click here to see answer by bucky(2189)

Question 89026: what are the conditions needed for the graph of a rational functio to have a vertical asymptote?
Click here to see answer by stanbon(57228)

Question 89244: what is the value of the expression 3x^2y/xy^2 when x= 7 and y= 4
a. 7/3
b. 21/4
c. 2/12
d. 3/4
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89242: simplify the rational expression x-6/x^2-36
a. x-6
b. 1/x+6
c. x+6
d. 1/x-6
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89248: divide: p^2+4p-5/p^2+7p+10 × p+4/p-1
a. 2
b. p+2
c. p+4/p+2
d. p+2/p+4
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89246: divide: x^2-1/x^2+3x+2 ÷ x^2+2x-3/x^2+x-2
a. x-1/x+3
b. x+1/x+3
c. x+3/x-1
d. x-1/x+1
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89241: simplify the rational expression x^2+6x-16/x^2+18x+80
a. x-2/x+10
b. x-10/x+2
c. x+2/x-10
d. x+10/x-2
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89245: what are the non-permissible values of the rational expression 4xy/4x^2y^2?
a. x=0 and y=1
b. x=0 and y=0
c. x=4 and y=-1
d. x=2 and y=-2
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89243: which of the following statements would represent a non-permissible value for the expression x/x+y?
a. x=y
b. x=0
c. x=2y
d. x= -y
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89240: simplifiy the rational expression x^2-49/x-7
a. 1/x-7
b. 1/x+7
c. x+7
d. x-7
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89239: which of the following is equivalent to the rational number 4xy/5y^2?
a. 4/5
b. 4x/5y
c. 8y/12y^2
d. 4x/y
Click here to see answer by malakumar_kos@yahoo.com(315)

Question 89384: divide 35q^9/9q^5 ÷ 25q^6/10q^5
a. 18/175q
b. 175q^4/18
c. 9q^6/14
d. 14q^2/9
Click here to see answer by checkley75(3666)

Question 89391: what are the non-permissible values for the rational expression x^2-4/y^2-4
a. y=0 and y=1
b. y=4 and y=-4
c. y=0 and y=3
d. y=2 and y=-2
Click here to see answer by bucky(2189)

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