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
spayn [35]
3 years ago
7

How do I find the range of this rational function, how do I do the steps in order to find it, please help!!!​

Mathematics
2 answers:
Sindrei [870]3 years ago
8 0

Answer:

Range= (0,∞) and (-∞,0)

Step-by-step explanation:

Theres no real process to finding this out you just look at what type of function you have, your graph and your asymptote. We can see that the parts above the asymptote go up and towards ∞ and the part below goes down to -∞ but they can not cross 0

ad-work [718]3 years ago
3 0

Answer:

(-infinity, -32/81] U (0, positive infintiy).

( use the sideways 8 symbol for infinity).

Step-by-step explanation:

The range is all possible y values in a function.

We can find the inverse of the function to find the range.

y =  \frac{8}{ {x}^{2} - 7x  - 8 }

Replace x with y

x =  \frac{8}{ {y}^{2} - 7y - 8 }

Write the LCD as two binomial,

x =  \frac{8}{(y + 1)(y - 8)}

Multiply both sides by both binomial

x(y + 1)(y - 8) = 8

(xy + x)(y - 8) = 8

x {y}^{2}  - 8yx + xy - 8x = 8

xy {}^{2}  - 8yx + xy = 8 + 8x

y( {x}^{2}  - 8x + x) =  8 + 8x

\frac{8 + 8x}{ {x}^{2} - 7x }

{x}^{2}  - 7x = 0

{x}^{2}  - 7x  + 12.25 = 12.25

(x - 3.5) {}^{2}  = 12.25

(x - 3.5) = 3.5

x = 3.5

Plug that in to the function to find it range.

We get approximately

-  \frac{35}{81}

So this means a point on our function must include -35/81.

The vertical asymptote is 0 so our y cannot be zero but it goes infinitely up so our range is

(-infinity, -32/81]U (0, positive infintiy).

<em>(</em><em> </em><em>use</em><em> </em><em>the</em><em> </em><em>sideways</em><em> </em><em>8</em><em> </em><em>symbol</em><em> </em><em>for</em><em> </em><em>infinity</em><em>)</em><em>.</em>

You might be interested in
X + 8 = 10 solve by subtraction
eduard
The answer to this is:
x=2
8 0
3 years ago
Rosa works due north of home. Her husband Ray works due east. They leave for work at the same time. By the time Rosa is 5 miles
vlabodo [156]
 Ray is 12 miles from home.

Let x be Ray's distance from home.  His distance is one leg of a right triangle; 5, Rosa's distance from home, is the other.  The hypotenuse, the distance between them, is 1 more than Ray's distance from home, or x+1.  Using the Pythagorean theorem,

5²+x²=(x+1)²
25+x²=(x+1)(x+1)

Multiplying the binomials, we have
25+x²=x*x+1*x+1*x+1*1
25+x²=x²+1x+1x+1
25+x²=x²+2x+1

Subtracting x² from both sides,
25 = 2x+1

Subtracting 1 from both sides,
24 = 2x

Divide both sides by 2, and we have
12 = x

Ray is 12 miles from home.
5 0
3 years ago
Which numbers are irrational ?
lianna [129]

Answer:

1.true  2.False  3. true 4. False  5. true 6. false

Step-by-step explanation:

Irrational number are with the square root sign

8 0
3 years ago
Select all equations that match the solution for this equation: 5(x - 12) = 20
mixer [17]

Answer:

The answer is x=16 so whatever the equations should look like it should be this:

Step-by-step explanation: 5(x-12)=20 5x-60=20 add 60 to 20 and get 5x=80 x=16

5 0
3 years ago
Linda enrolls for 10 credit-hours for each of two semesters at a cost of $500 per credit-hour (tuition and fees). In addition, t
kodGreya [7K]
I agree with the other answer
3 0
3 years ago
Other questions:
  • Every day Jordan is paid an hourly wage plus a flat fee for transportation expenses based on the graph how much is Jordan paid p
    7·2 answers
  • How to find missing angles parallel
    9·1 answer
  • Y+9=-3(x-2) standard form
    9·1 answer
  • Below are the steps to solve an equation:
    15·1 answer
  • In a random sample of ​people, the mean driving distance to work was miles and the standard deviation was miles. Assume the popu
    8·1 answer
  • H(6)=<br><br><br><br><br><br> PLEASSSEEEE HELP IN 10 min NEED IT NOW
    5·1 answer
  • 5(x+2)=⅗ (5+10x) <br> how do i solve
    5·1 answer
  • Evaluate the function for an input of 0.
    12·1 answer
  • 3^2(3^3)^2.3^-8 simplify
    10·1 answer
  • What is the value of the expression below when Z =7 <br> 3z- 3
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!