# Math- Rational Functions

137,097 results

### Calculus

We're learning about different kinds of functions and I don't really understand the difference between rational and algebraic functions. I know that rational functions are functions that are a ratio of two polynomials, and algebraic functions are any functions that can be made...

### MATH _ GRAPHING RATIONAL FUNCTIONS

When graphing rational functions, how do I know which directions the graphs go? Example, for equation y = 9/x - x, how would you graph this? Also, why is the horizontal asymptote for f(x)= 2+x / x-7 is 1 instead of 0?

### Math- Rational Functions

1. Some rational functions have asymptotes, others have holes, and some have both. Explain how you can identify, without graphing, which graphical features a rational function will have. Can someone explain this thoroughly ? I don't understand. thanks in advance.

### Gr.11 - Rational functions graphing.

1. Identify a rational function whose graph is a horizontal line except for two holes. Graph the function. 2. Identify a rational function who graph lies entirely above the x-axis and has a single vertical asymptote. Graph the function. 3. Identify a rational function who ...

### math

hello, i have some question about rational functions. 1) are there any sites that are good in teaching graphing rational functions? 2) for the domain of the rational function it is what the denominator cannot equal to rite? for example the denominator of x^2-7x+10 can be ...

### calculus: Rational Functions

I do not understand how to complete rational functions: ie: As x (arrow) -3, f(x) (arrow) ?. Our book sucks and our instructor is little help. Thank you.

### Math Rational Functions-Please Clarify =)

I have a question about the rational function I recently posted. Would the range still be (-∞,2)U(2,∞) if the rational function is what Reiny posted "(2x^2-18)/(x^2+3x-10)." The y-intercept confuses me because its (0,1.8) and when I look at the line it passes ...

### Math

For the given functions, write the rational function, r(x) = [f(x-h)-f(x)]/h and simplify: a. F(x) = 2x+3 b. F(x) = 1/(x+1) c. F(x) = x^2 --- Just need to know that the rational function is and maybe I can do the questions. Thanks.

### Pre-Calculus

Rational Functions y = (x^2+7x-4)/(x-2) Since the degrees of both the numerator and denominator are the same, I would use the leading coefficient, and both the rational functions start with 1, so would the horizontal asymptote be 1? Also don't get how to find the horizontal ...

### Algebra

Graph and label the following two functions: f(x)=(x^2+7x+12)/(x+4) g(x)=(-x^2+3x+9)/(x-1) 1. Describe the domain and range for each of these functions. 2. Determine the equation(s) of any asymptotes found in the graphs of these functions, showing all work. 3. Discuss the ...

### Math advance functions gr 12

Using rational functions solve 7+ 1(numerator) x (denominator) = 1 (numerator) x-2(demominator)

### advance functions gr12 HELP ASAP

using rational functions solve (x+5)/(x-3)= (2x+7)/(x) thank you

### advance functions gr12 HELP ASAP

Using rational functions solve 7+ (1)/x = 1/(x-2) thank you

### Math-Rational #'s

Just trying to understand this. Please let me know if I did these right. Thanks!!! -7 as a rational # = -7/10 -3.03 as a rational # = -33/10 -2 3/12 as a rational # = -25/12 1.03 as a rational # = 13/10

### advance functions gr12 (SORRY LAST ONE HAD A TYPO)

Using rational functions solve 7+ (1)/x = 1/(x-2)

### advance functions gr12

Using rational functions solve (7+ 1)/x = 1/(x-2)

### Math

Use your knowledge of exponents to solve. a) 1/2^x=1/(x+2) b) 1/2^x>1/x^2 So I know that these functions are rational functions.. and I am trying to solve for x. I tried to solve them by I keep getting stuck with the exponent 2 which is the exponential function.. Help please

### rational functions

A rational function that passes through (0,0) and (4, 8/7) has the x-axis as a horiztonal asympotote. It also has 2 vertical asymptotes x=3, x=-3. I understand that to set it up, it is y= ax+b / (x+3)(x-3). I don't understand how to solve for a and b.

### rational functions... PLEASE HELPPPPP

A rational function that passes through (0,0) and (4, 8/7) has the x-axis as a horiztonal asympotote. It also has 2 vertical asymptotes x=3, x=-3. I understand that to set it up, it is y= ax+b / (x+3)(x-3). I don't understand how to solve for a and b.

### Math Rational Functions

What is the domain and range of 2x^2-18/x^2+3x-10

### advance functions gr 12

Using rational functions solve 3(numerator) 2x-4 (denominator) < (with a "-" underneath) 4 (numerator) x-2(demominator)

### Math rational exponents

what is the domain of these functions? y= -1/5x^(-1/3) and y=10x^ (-1/6)

### advance functions gr 12

Using rational functions solve x+5(numerator) x-3 (denominator) = 2x+7 (numerator) x(demominator)

### advance functions gr 12

Using rational functions solve x+5(numerator) x-3 (denominator) = 2x+7 (numerator) x(demominator)

### advance functions gr 12

Using rational functions solve 7+ 1(numerator) x (denominator) = 1 (numerator) x-2(demominator)

### Math

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0. A. horizontal asymptotes B. polynomial C. vertical asymptotes D. slant asymptotes Is the answer D. vertical asymptotes?

### Algebra 1

Which values should I use to graph the rational function y = 1/x-2 - 6? (The asymptotes are x = 2; y = -6.) Also, what method could I use to choose values for graphing rational functions?

### Algebra 1

Which values should I use to graph the rational function y = 1/x-2 - 6? (The asymptotes are x = 2; y = -6.) Also, what method could I use to choose values for graphing rational functions?

### Rational Functions

Write an equation for a rational function whose graph has the following properties: x-intercept of 3 y-intercept of -3 vertical asymptote of x=-2 horizontal asymptote of y=2

### Math (calc)

Given the function: f(x)=x^3(x-2)^2 , on the interval [-1,3] find the domain and Asymptotes ...Isn't the domain (-1<x<3) ? and as for the asymptotes I thought you could only find them for rational functions and since that function is not rational I guess there aren't any...

### ****college algebra…radical functions****

Create a rational function such that the graph of has vertical asymptotes at x=5 and x= -7, a hole at x=2 , and a horizontal asymptote at y = 14. By creating a rational function, you are to write rule for this function. There are many correct solutions here.

### m240

All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) ≠ 0. A. horizontal asymptotes B. polynomial C. vertical asymptotes D. slant asymptotes My answer is B is this correct.

### Math

2-4 paragraphs plus two graphs Details: Many different kinds of data can be modeled using polynomial functions. An example of a polynomial function would be gas mileage for an automobile. If we compare gas mileage at two different speeds, V1 and V2, the gas required varies as...

### Math

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of ...

### Math

1. Is square root of negative 10 irrational or rational? 2. Is 2.79797979... irrational or rational? I'm not very good at identifying irrational and rational numbers at least I tried too. 1. irrational 2. rational

### math advanced functions grade 12

Find the solution set to the following rational inequality, 240/x+8 > 20x/x+1

### math

What is the best sequence of names to identify this set of numbers? (1 3/5,-10, 0.51(the one is repeating), TT,17) 1.(rational,integer,irrational,irrational,natural) 2. (rational,irrational,rational, irrational, whole) 3.rational,real,rational,real, natural) 4. (real,integer, ...

### math- please help

What is the best sequence of names to identify this set of numbers? (1 3/5,-10, 0.51(the one is repeating), TT,17) 1.(rational,integer,irrational,irrational,natural) 2. (rational,irrational,rational, irrational, whole) 3.rational,real,rational,real, natural) 4. (real,integer, ...

### Functions

what is the oblique asymptote of this rational function: (x ^ 3) / (x ^ 2+1)

### Math

Will the values described in each situation be rational or irrational? Select Rational or Irrational to describe each situation.I put "R" and "I" to represent the choices I choose. the length of a rectangle with a rational area and irrational width :R the area of a circle with...

### Math

I just wanted to check my answers with anyone willing to take the time. Identify all sets that -3/4 belongs to: a.whole #s, integers, rational #s b.rational #s c.integers, rational #s d.odd #s, whole #s, integers, rational #s Ithought it was C How many centimeters are equal to...

### Algebra II

Give the equations of any vertical asymptotes for the graphs of the rational functions. f(x)=(x-4)/(x²+7)

### Algebra II

Give the equations of any vertical asymptotes for the graphs of the rational functions. f(x)=(x-4)/(x²+7)

### advanced functions

simplify the rational expression x^4+3x^3-2x^2-6x/x^3-2x stating all restrictions on the variable.

### Algebra II

Give the equations of any vertical asymptotes for the graphs of the rational functions. f(x)=(3x³+6x-6)/(x²+3x-10)

### Algebra

Using the index of a series as the domain and the value of the series as the range, is a series a function? Include the following in your answer: Which one of the basic functions (linear, quadratic, rational, or exponential) is related to the arithmetic series? Which one of ...

### Algebra II

Give the equations of any horizontal asymptotes for the graphs of the rational functions. h(x)=(7x²-8x-5)/(8x²-3x+9) g(x)=(x²+4x-8)/(x-8)

### Math

Which set of numbers best describes the displayed weights on a digital scale that shows each weight to the nearest half of pound. A) Whole B) Rational C) Real D) Integers My answer is Rational because rational numbers can be written as a decimal or fraction where a/b. Thanks

### Math

If the inverses of two functions are both functions, will the inverse of the sum or difference of the original functions also be a function? Explain your reasoning.

### Math(dispute to previous question)

2)Name the sets of numbers to which 457 belongs. (answer)natural,whole,integers,rational,reals My book says that every REAL number has to be rational or irrational. Blueridge said that my answer was correct except to exclude rational from my list. From what my book says I HAVE...

### Math

Can you check my work and tell me if I did anything wrong? 1. With the functions: f(x) = x^2 + 3x and g(x) = -3 + x what is f(x) + g(x)? Answer: x^2 + 4x - 3 2. With the functions: f(x) = x + 4 and g(x) = x -3 what is (f*g)(x)? Answer: x^2 + x - 12 3. With the functions: f(x...

### Functions in Math

Im looking at internet sites and Im not quite understanding functions. I have a question like; A function f(x) has the properties i) f(1) = 1 ii) f(2x) = 4f(x)+6 Could you help me out. I know nothing about functions.

### rational functions

If f(x) is a polynomial function, does 1/f(x) always have a horizontal asymptote? Explain why or why not and provide a counterexample if needed.

### Adv functions

Given that the cubic equation has rational coefficients and has the root , determine the values of a and b. I got a=2 and b=4. But the answer is a=-6 and b=-20

### Math

Identify al the sets to which the number 3.1214122144...belongs. A.) Rational** B.) Irrational C.) Integer, Rational D.) Whole number, Integer, Rational

### math

HELP. Help I have to decide whether these are rational or irrational. .73737373... .61611611161111..... 1/23 Can someone explain this to me? Rational numbers are just fractions. The decimal expansion of fractions will either terminate or it will become periodic after a while. ...

### 9th grade

Name the set(s) of numbers to which 1.68 belongs. a. rational numbers b. natural numbers, whole numbers, integers, rational numbers c. rational numbers, irrational numbers d. none of the above my answer a)rational numbers

### Pre-algebra

Jeremy is playing a game called “Rational Round Up” where he has to collect all the numbers in a maze that are rational and then get to the end of the maze. When he collects a number he must prove it is rational by writing it as a quotient of two integers. Help him ...

### Maaaaath

When graphing rational functions, how do I know which directions the graphs go? Example, for equation y = 9/x - x, how would you graph this? Also, why is the horizontal asymptote for f(x)= 2+x / x-7 is 1 instead of 0?

### Math - Rational Roots

1.) What are the possible rational roots of the function f(x) = 3x^4 - x - 2 2.) What are the rational roots of the following equation: x^3 - 4x^2 - 4x +16 = 0 Thank you for any help!

### Intermediate Algebra (math)

(8x^2y^2+4xy^2-12y^2) ÷ 4xy^2 I received this problem. I was told to divide the rational expression. The problem I am having is I feel like something is missing. I only understand to divide rational expressions we take the first rational expression and multiply it by the ...

### Intermediate Algebra (math)

(8x^2y^2+4xy^2-12y^2) ÷ 4xy^2 I received this problem. I was told to divide the rational expression. The problem I am having is I feel like something is missing. I only understand to divide rational expressions we take the first rational expression and multiply it by the ...

### Math

Rewrite the following exponential functions as logarithmic functions, and the logarithmic functions as exponential functions a) f(x)=(7/8)^x b) f(x)=log12x c) f(x)=log5/9x

### Math

Rewrite the following exponential functions as logarithmic functions, and the logarithmic functions as exponential functions: f(x)=(7/8)^x b) f(x)=log12x c) f(x)=log5/9x

### math

classify the following number as rational or irrational: 4.1 My guess is Rational

### math help

how do prove that this equation has rational roots for all rational values of K 3x^2+kx-k=3x

### advanced functions/precalculus

1. The function f(x) = (2x + 3)^7 is the composition of two functions, g(x) and h(x). Find at least two different pairs of functions g(x) and h(x) such that f(x) = g(h(x)). 2. Give an example of two functions that satisfy the following conditions: - one has 2 zeros - one has ...

### Math

Identify all sets to which the number 3 belongs A. Whole numbers, integers, rational numbers B. Rational numbers C. Integers, rational numbers D. Even numbers, whole numbers, integers, rational numbers I THINK IT'S A

### math

which statement is false? A: 3.648 reapeating=is rational B:-3 2/13=rational

### Math

Find all possible rational roots using the rational root theorem. x^4 - 3x^2 + 12 = 0 Plus/minus 1, 2, 3, 4, 6, 12?

### Math-Measure's & area

1. Find the area of a parallelogram with base b and height h. B=82cm H=16.6cm a.**1,361.2 cm^2 b.6,724 cm^2 c.137.78 cm^2 d.98.6 cm^2 2.Identify all the sets to which the number belongs. Choose from rational number, irrational number, whole number, and integer. 0.123333... a....

### 6TH GR. ALGEBRA

EXTENDING THE LESSON If you add any two rational numbers, the sum is always a rational number. So, the set of rational numbers is closed under addition. Is the set of rational numbers closed under subtraction. multiplication,and division also? Explain.

### math,help,bobpursly

What are some challenges for rational expressions? Also on my previous question about why are polynomials important bobpursly can you expalin it to me towards what you ment about your responce because i still do not undertand...thanks when you get a chance. Polynomials are ...

### math help me!!

is square root of 56 a rational number? explain uranswer using what you know about rational and irrational numbers. thnx alot!

### algebra1

I have a question does anyone have the Rational Expressions and Functions Unit Test questions and answers?? If you can you plzz help me out i am almost done

### Math Check Pleas Thank You

1. Which of the following numbers is an example of an integer? 15 * 0.252525 . . . 3/5 (fraction) Square root of 7 2. Which statement is false? Every integer is a real number. The number zero is a rational number. Every irrational number is a real number. Every real number ...

### math

If a b c are non zero,unequal rational numbers then prove that the roots of the eqn (abc²) x²+ 3a²cx+b²cx-6a²-ab+2b²=0 are rational.

### math

Which statement is true? A. All irrational numbers are also rational numbers. B. Half of the irrational numbers are also rational numbers. C. One-third of the irrational numbers are also rational numbers D. Irrational numbers cannot be classified as rational numbers. Is the ...

### Calculus

Find the sum and difference functions f + g and f – g for the functions given. f(x) = 2x + 6 and g(x) = 2x - 6 f(x) = x^2 - x and g(x) = -3x + 1 f(x) = 3x^3 - 4 and g(x) = -x^2 + 3 State the domain and range for the sum and difference functions in #3. Find the product and ...

### math

List all possible rational zeros of... h(x)= 2x to the (4th power) - 5x (to the third power) + 3x (to the 2nd power) + 4x - 6 Use the Rational Roots Theorem. Any root of the form p/q with p and q relatively prime must be such that p divides 6 and q divides 2. You then find the...

### Math

Which statement is false? A. The number zero is a rational number. B. Some irrational are also rational numbers. C. Every irrational number is a real number. D. Every integer is a rational number Is the answer C?

### College Algebra

Given the following rational functions,find:a.)the horizontal asymptote(s), b.)the vertical asymptote(s), if any,and c.) the oblique asymptote(),if any. f(x)=x(x-17)^2/(x+12)^3

### Precalculus

I'm HOPING this is the last problem I need help on.. :-/ List the possible rational zeros of f using the rational zero theorem. f(x) = 2x^3 - x^2 + 5x + 6 I applied the rational zero theorem, but none of the factors worked :(

### discrete math

1)prove that if x is rational and x not equal to 0, then 1/x is rational. 2) prove that there is a positive integers that equals the sum of the positive integers not exceeding it. Is your proof constructive or nonconstructive? For 1) use the definition of a non-zero rational ...

### Geomatry

For each of the rational functions find: a. domain b. holes c. vertical asymptotes d. horizontal asymptotes e. oblique asymptotes f. y-intercept g. x-intercepts 1. f(x)= x^2+x-2 / x^2-x-6

### algebra

For each of the rational functions find: a. domain b. holes c. vertical asymptotes d. horizontal asymptotes e. oblique asymptotes f. y-intercept g. x-intercepts 1. f(x)= x^2+x-2 / x^2-x-6

### Calculus

Which of these rational functions has a ) horizontal asymptote? a slant asymptote? no vertical asymptote? r(x)= 2x-1/ x^2-x-2 = 2x-1/ (x-2)(x+1) s(x)= x^3+27/x^2+4 = (x+3)(x^2-3x+9)/(x-2)(x+2) t(x)=x^3-9x= x(x-3)(x+3)/x+2 u(x)=x^2+x-6/x^2-25= (x+3)(x-2)/(x+5)(x-5) I do not ...

### math test

Hi! I have a math test coming up tomorrow, and I need to prepare. but,i don't know how I should. . . any help would be great. she told us to: Be prepared to identify and explain functions, linear functions and proportional functions. Be prepared to use the new function ...

### PLEASE CHECK MATH TY!

1. Which of these numbers can be classified as both real and rational? A. 1/2 *** B. -1.016879413894 C. √5 D. 0.89089908999 2.Which is both a real number and an integer? A. √7 B. 0.15 C. -15 *** D. 1/3 3. What is an example of an irrational number? A. -√16 B. √25 C...

### algebra

Find the LCD for the given rational expressions, and convert each rational expression into an equivalent rational expression with the LCD as the denominator. 4/x-y , 5/2y-2x

### Calculus

Math questions, please help me? :(? Find the composite functions f o g and g o f for the given functions. f(x) = 10^x and g(x) = log x State the domain and range for each: f(x) = 4x + 1 and g(x) = x^2 f(x) = sin x and g(x) = x^2 - x + 1 f(x) = 10^x and g(x) = log x If f = {(-2...

### Math 11 - Rational Expressions

I really don't understand how you find or identify the restrictions at all for rational expressions, can someone talk me through it? I have a math exam Monday and I'm stressed. Thanks. Here are some examples for my textbook if needed... 1) 2x + 1 / 2x - 1 2) x-5 / x^2 + 3x + 2...

### Math

Use the Rational Zeros Theorem to write a list of all possible rational zeros of the function. -2x^4+4x^3+3x^2+18

### functions

Identify a rational function whose graph is a horizontal line except for two holes. Graph function.

### algebra 1

i need help with algebra 1 unit 6 rational expressions and functions. lesson 3 dividing polynomials need answers

### math

which statement is false: A: 3.648 reapating 8= is rational B:-3 2/13= is rational C: 3.605551275464...=is irrational D: -3.744= is irrational

### MATH HELP PLEASE

Which statment is false? A. The number zero is a rational number. B. Some irrational numbers are also rational numbers. C. Every irrational number is a real number D. Every integer is a rational number Is the answer C?

### Math

Proove that: a)2^(1/2) is not rational. b) prove that 2^(1/3) is not rational. I have managed to prove the first part, but i am stuck on the second can someone give me an hint please?

### Algebra

Which of the following statements is false? The sum of two rational numbers is always rational. The sum of a rational number and an irrational number is always rational. The product of a nonzero rational number and an irrational number is always irrational. The product of two ...