All categories

3 years ago

Write a rational function with no vertical asymptotes and no holes. Please explain.

Mathematics

1 answer:

Ksju [112]3 years ago

4 0

ANSWER

$f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 }$

EXPLANATION

We write the function such that both the numerator and the denominator are prime.

An example of a rational function with no vertical asymptotes and no holes is

$f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 }$

For the above rational function, the denominator is never zero, so there are no vertical asymptotes.

Also the highest common factor for the numerator and the denominator is 1 so there are no holes.

You might be interested in

Construct a quadratic polynomial whose zeroes are negatives of the zeroes of the

sp2606 [1]

Given:

The given quadratic polynomial is :

$x^2-x-12$

To find:

The quadratic polynomial whose zeroes are negatives of the zeroes of the given polynomial.

Solution:

We have,

$x^2-x-12$

Equate the polynomial with 0 to find the zeroes.

$x^2-x-12=0$

Splitting the middle term, we get

$x^2-4x+3x-12=0$

$x(x-4)+3(x-4)=0$

$(x+3)(x-4)=0$

$x=-3,4$

The zeroes of the given polynomial are -3 and 4.

The zeroes of a quadratic polynomial are negatives of the zeroes of the given polynomial. So, the zeroes of the required polynomial are 3 and -4.

A quadratic polynomial is defined as:

$x^2-(\text{Sum of zeroes})x+\text{Product of zeroes}$

$x^2-(3+(-4))x+(3)(-4)$

$x^2-(-1)x+(-12)$

$x^2+x-12$

Therefore, the required polynomial is $x^2+x-12$ .

4 0

3 years ago

Write a linear function that relates y to x <br><br> y=

son4ous [18]

y=x-2

hope this helped :)

7 0

2 years ago

Adam drove 280 miles in 4 hours. On average, how fast did he drive in hours per mile? Express your answer in simplest form.

Natasha2012 [34]

Answer:

1/70 hours per mile

Step-by-step explanation:

We want hours per mile

Take the hours and divide by the miles

4 hours / 280 miles

1 hours/ 70 miles

7 0

3 years ago

Read 2 more answers

A grade has 81 girls and 72 boys. The grade is spilt into groups that have the same ratio of boys to girls as the whole grade. H

MariettaO [177]

There are 81 girls to every 72 boys in total, which can be represented by 81/72, which put into decimal form, is 1.125. If you then take the number of boys in the group, 16, and multiply it by this number (because the problem states that the ratio is constant) you can find the number of girls in the group.

16*1.125=18

So there are 18 girls in a group with 16 boys.

4 0

3 years ago

Read 2 more answers

A bag contains tiles of different colors. Jackson randomly selects a tile from the bag and returns the tile to the bag after rec

quester [9]

Answer:

2/15

Step-by-step explanation:

The answer choices to this question do not make sense since probability is a measure that is always <= 1.0

Based on the number of times a particular colored tile is drawn we can assume that at the minimum there are 6 green, 20 red, 7 blue, 8 purple and 4 black tiles

Total number of tiles = 6 + 20 + 7 + 8 + 4 = 45

Probability of drawing a green tile = 6/45 = 2/15

3 0

2 years ago