Mathematics, 20.12.2019 14:31 haileyw123

Determine any asymptotes (horizontal, vertical or oblique). find holes, intercepts and state it's domain.

Answers: 3

Show answers

Answers

Answer from: johnsonkia873

Horizontal Asymptote is y = 0

Vertical Asymptote is x = -4

No Slant Asymptote

Hole at (5, 0.14)

x-intercepts:

x-intercept $(-\frac{1}{2},0)$

y-intercepts:

y-intercept $(0,\frac{1}{16})$

Domain is ${x|x\neq -4,5}$

Step-by-step explanation:

1. Horizontal Asymptotes

* If the degree of the numerator is less than the degree of the denominator (this is our case since multiplying will give the numerator a degree of 2 and denominator a degree of 3), then y = 0 is the only horizontal asymptote

Horizontal Asymptote is y = 0

2. Vertical Asymptotes

* To get VA (vertical asymptote), we set the denominator equal to zero.

Before doing this, we see that we can cancel out (x-5) from both numerator and denominator so the denominator becomes (x+4)^2. Now we find VA:

$(x+4)^2=0\\x+4=0\\x=-4$

Vertical Asymptote is x = -4

3. Oblique asymptotes

* If the degree of numerator is less than the degree of the denominator (this is our case as explained above), then there is no slant asymptote.

No Slant Asymptote

4. Holes

There is hole in a rational function if there is the same factor in both numerator and denominator (before simplifying, only after factoring). Set that equal to 0 and solve. Then, cross out the common factor and put the x-value into the function and get the y-value of the hole.

We can see that there is a factor of (x-5) in both the numerator and denominator. We set it equal to 0 and solve for x:

$x-5=0\\x=5$

Putting x = 5, we get:

Y value of hole = $g(x)=\frac{2x+1}{(x+4)^2}\\g(5)=\frac{2(5)+1}{(5+4)^2}\\g(5)=0.14$

Hole at (5, 0.14)

5. Intercepts

To get x-intercepts, we set y = 0 (g(x) = 0) and for y-intercepts we set x = 0.

x-intercepts:

$0=\frac{2x+1}{(x+4)^2}\\2x+1=0\\2x=-1\\x=-\frac{1}{2}$

x-intercept $(-\frac{1}{2},0)$

y-intercepts:

$y=\frac{2x+1}{(x+4)^2}\\y=\frac{2(0)+1}{(0+4)^2}\\y=\frac{1}{16}$

y-intercept $(0,\frac{1}{16})$

6. Domain

This is the set of allowed x-values of the function. We simply disregard any value that would make the denominator equal to 0.

So we have:

x - 5 = 0, x = 5

and

(x+4)^2 = 0, x = -4

Domain is the set of all real numbers x EXCEPT x = -4 and x = 5

Domain is ${x|x\neq -4,5}$

Answer from: Quest

1195 was the store owner's profit.

Answer from: Quest

answer: you need to organize this better it does not make sense.

step-by-step explanation: ?

Another question on Mathematics

Mathematics, 21.06.2019 15:10

12x + 1 = 25 solve the following equation. then place the correct number in the box provided.

Answers: 2

Answer

Mathematics, 21.06.2019 18:00

Pls if a cow has a mass of 9×10^2 kilograms, and a blue whale has a mass of 1.8×10^5 kilograms, which of these statements is true?

Answers: 3

Answer

Mathematics, 21.06.2019 20:30

This is about circle theorems. someone asap : (

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Zack notices that segment nm and segment pq are congruent in the image below: which step could him determine if δnmo ≅δpqr by sas? (5 points) segment mo ≅ segment qr segment on ≅ segment qp ∠ n ≅ ∠ r ∠ o ≅ ∠ q

Answers: 3

Answer

You know the right answer?

Determine any asymptotes (horizontal, vertical or oblique). find holes, intercepts and state it's do...

Questions

Mathematics, 29.10.2020 01:20

A hot air balloon ascended at the rate of 400 feet per hour for 3 hours and 15 minutes. What was the total distance that the balloon ascended?...