1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ollegr [7]
3 years ago
11

How are rational functions similar to linear, quadratic, or exponential functions? How are they different? When are these simila

rities or differences important when looking for intersections between rational functions and other types of functions? Be sure to cite examples as you explain your ideas.
Mathematics
1 answer:
jeyben [28]3 years ago
7 0

Answer:

See explanation below for further details.

Step-by-step explanation:

A rational consist of two real numbers such that:

\frac{a}{b} =c

If c is a polynomial with a certain grade, then, both the numerator and the denominator must be also polynomials and the grade of the numerator must be greater than denominator.

If c is linear function, that is, a first order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example:

If a = x^{2} and b = x, then:

c = \frac{x^{2}}{x}

c = x

If c is a quadratic function, that is, a second order polynomial, then a must be a (n+1)-th polynomial and b must be a n-th polynomial.

Example

If a = 3\cdot x^{3} and b = x, then:

c = \frac{3\cdot x^{3}}{x}

c = 3\cdot x^{2}

But if c is an exponential, both the numerator and the denominator must be therefore exponential function and grade of each exponential function must different to the other.

Example

If a = 10^{2x} and b = 3\cdot 10^x, then:

c = \frac{10^{2\cdot x}}{3\cdot 10^{x}}

c = \frac{1}{3}\cdot 10^{2\cdot x -x}

c = \frac{1}{3}\cdot 10^x

Otherwise, c would be equal to a constant function, that is, a polynomial with a grade 0.

If a = 5\cdot e^{x} and b = -3\cdot e^{x}, then:

Example

c = \frac{5\cdot e^{x}}{-3\cdot e^{x}}

c = -\frac{5}{3}

It is worth to add that exponential functions can be a linear combination of single exponential function, similar to polynomials.

Example

5\cdot a^2\cdot x -9

You might be interested in
Which ordered pair represents a solution to f(x) = x – 5 if f(−1)?
olchik [2.2K]

Answer:

(-1, -6)

Step-by-step explanation:

f(x) = x - 5

f(x) = -1-5

f(x) = -6

(-1, -6)


4 0
3 years ago
Read 2 more answers
Solve for y 9x - y = -6x + 4y
Lyrx [107]

Answer:

y = 3x

Step-by-step explanation:

Given

9x - y = - 6x + 4y ( subtract 4y from both sides )

9x - 5y = - 6x ( subtract 9x from both sides )

- 5y = - 15x ( divide both sides by - 5 )

y = 3x

4 0
3 years ago
Read 2 more answers
1.
Vesnalui [34]
X is 125 as well because it’s an Cubs all sides are equal
4 0
2 years ago
What is the simplest form of 13/14
OleMash [197]
13/14 is already in simplest form because they have no common factors.
7 0
3 years ago
Read 2 more answers
In a box of marbles, the ratio of red marbles to total marbles is 2:5. the ratio of green marbles to total marbles is 3:10. if t
STALIN [3.7K]
Ratio:

Red : Total 
  2   :    5
 (x2)    (x2)
  4   :   10

Green : Total
  3   :       10

Total of red and green marbles = 4 + 3 = 7

Blue marbles = 10 - 7 = 3

10 parts = 40 marbles
1 part = 40 ÷ 10 = 4
3 parts = 4 x 3 = 12

Answer: There are 12 blue marbles.
7 0
2 years ago
Other questions:
  • Suppose y varies directly with x. Write a direct variation equation that relates x and y. y=7 1/2 when x=3
    8·1 answer
  • Whats 2+2 fhelllllllll-pppppppppp
    9·2 answers
  • Would it be <br> A, B ,C or D
    8·1 answer
  • What is an expression that is four times as large as 52 minus 9.
    11·2 answers
  • 7 1/2 divided by 1 2/3
    7·2 answers
  • What is the scale factor from AABC to ADEF?
    13·1 answer
  • when graphing a system of equations with "the same"or "different" in order to make the sentence a true statement ______________.
    9·1 answer
  • every day of the week sam's swim shop offers a different deal to its loyal customers. if the total price neil paid was $92.30 an
    8·1 answer
  • Order 1.62, 16.2%, 15/20 from greatest to least
    5·2 answers
  • Emily earns $0.30 for every 0.75 mile she bikes. How much does she earn for 15 miles?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!