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
marissa [1.9K]
2 years ago
14

Find the domain and range of f(x)= (2x+6) / ((x^2)-x-12)

Mathematics
1 answer:
creativ13 [48]2 years ago
8 0

Answer:

Step-by-step explanation:

If you want to determine the domain and range of this analytically, you first need to factor the numerator and denominator to see if there is a common factor that can be reduced away.  If there is, this affects the domain.  The domain are the values in the denominator that the function covers as far as the x-values go.  If we factor both the numerator and denominator, we get this:

f(x)=\frac{2(x+3)}{(x-4)(x+3)}

Since there is a common factor in the numerator and the denominator, (x + 3), we can reduce those away.  That type of discontinuity is called a removeable discontinuity and creates a hole in the graph at that value of x.  The other factor, (x - 4), does not cancel out.  This is called a vertical asymptote and affects the domain of the function.  Since the denominator of a rational function (or any fraction, for that matter!) can't EVER equal 0, we see that the denominator of this function goes to 0 where x = 4.  That means that the function has to split at that x-value.  It comes in from the left, from negative infinity and goes down to negative infinity at x = 4.  Then the graph picks up again to the right of x = 4 and comes from positive infinity and goes to positive infinity.  The domain is:

(-∞, 4) U (4, ∞)

The range is (-∞, ∞)

If you're having trouble following the wording, refer to the graph of the function on your calculator and it should become apparent.

You might be interested in
Mason claims that he can cut a parallelogram into two right scalene triangle. Which diagram best supports his claim
kkurt [141]

Answer:

THE ANSWER IS OPTION B

Because it has angles and all of them are not the same measure

3 0
1 year ago
How much cm³ is it the cilinder?
pychu [463]

Answer:

one because it is cilinder

7 0
1 year ago
Read 2 more answers
(8.6x107)-(9.1x10-8)simplify
natima [27]

Answer:

  85,999,999.999 999 909

Step-by-step explanation:

The expression represents the difference of a relatively large number and one that is relatively small. That difference is approximately the value of the large number. The exact value requires 17 digits for its proper expression. Most calculators and spreadsheets cannot display this many digits.

<h3>Standard form</h3>

The numbers in standard form are ...

  86,000,000 = 8.6×10^7

  0.000000091 = 9.1×10^-8

<h3>Difference</h3>

Their difference is ...

  86,000,000 -0.000000091 = 85,999,999.999 999 909

In scientific notation, this is ...

  8.599 999 999 999 990 9×10^7

4 0
1 year ago
Segment MN has endpoints at M(-5, 4) and N(7, -5). What is the midpoint of MN???? PLZ HELP
Paha777 [63]
Theres a formula to find the midpoint it’s... (x1+x2)/2, (y1+y2)/2. You fill in the x’s and y’s to get (-5+7)/2 for x, which equals 1 and (4-5)/2 to get -0.5. (1, -0.5) is your answer

7 0
3 years ago
Lia has a dog and a cat. Together, the pets weigh 24 pounds. The dog weighs 2 times as much as the cat.
telo118 [61]

Answer:

The dog weighs 16 pounds, while the cat weighs 8 pounds

Step-by-step explanation:

Let's call the weight of the dog d, and the weight of the cat c.

d+c=24

d=2c

Substitute the second equation into the first:

(2c)+c=24

3c=24

c=8

d=24-8=16

Hope this helps!

3 0
3 years ago
Other questions:
  • Consider the parallelogram shown below whose area is 40 square centimeters and height is 8 centimeters. The
    6·1 answer
  • (Extra points)
    9·1 answer
  • (QUICK QUESTION) If you have 18 credits In the 12th grade Is it possible to get 23 by June 2019?? In one semester
    13·2 answers
  • What property is (3×4) 5 =(5×4) 3
    12·2 answers
  • How do you solve this problem?
    12·1 answer
  • 100 POINTS BRNLST! Solve the system of equations using the substitution method.
    7·1 answer
  • - 2 - 5x = -16 for x​
    8·1 answer
  • Please help me find the median to this table
    13·1 answer
  • . Give expressions ;
    6·1 answer
  • Helpppppppppppppppp fasttttttttttttttt pleaseeeeeeeee
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!