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
11Alexandr11 [23.1K]
3 years ago
5

Describe the behavior of the function ppp around its vertical asymptote at x=-2x=−2x, equals, minus, 2. ​

Mathematics
1 answer:
insens350 [35]3 years ago
6 0

Answer:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

Step-by-step explanation:

Given

p(x) = \frac{x^2-2x-3}{x+2} -- Missing from the question

Required

The behavior of the function around its vertical asymptote at x = -2

p(x) = \frac{x^2-2x-3}{x+2}

Expand the numerator

p(x) = \frac{x^2 + x -3x - 3}{x+2}

Factorize

p(x) = \frac{x(x + 1) -3(x + 1)}{x+2}

Factor out x + 1

p(x) = \frac{(x -3)(x + 1)}{x+2}

We test the function using values close to -2 (one value will be less than -2 while the other will be greater than -2)

We are only interested in the sign of the result

----------------------------------------------------------------------------------------------------------

As x approaches -2 implies that:

x -> -2^{-} Say x = -3

p(x) = \frac{(x -3)(x + 1)}{x+2}

p(-3) = \frac{(-3-3)(-3+1)}{-3+2} = \frac{-6 * -2}{-1} = \frac{+12}{-1} = -12

We have a negative value (-12); This will be called negative infinity

This implies that as x approaches -2, p(x) approaches negative infinity

x->-2^{-}, p(x)->-\infty

Take note of the superscript of 2 (this implies that, we approach 2 from a value less than 2)

As x leaves -2 implies that: x>-2

Say x = -2.1

p(-2.1) = \frac{(-2.1-3)(-2.1+1)}{-2.1+2} = \frac{-5.1 * -1.1}{-0.1} = \frac{+5.61}{-0.1} = -56.1

We have a negative value (-56.1); This will be called negative infinity

This implies that as x leaves -2, p(x) approaches negative infinity

x->-2^{+}, p(x)->-\infty

So, the behavior is:

x->-2^{-}, p(x)->-\infty and as x->-2^{+}, p(x)->-\infty

You might be interested in
Please help with these questions!!!
klasskru [66]

Answer:

Step-by-step explanation:

Q1: (x-1) * (x+1) * (x-2) * (x+2)

Q2: x'1 = -1/3, x'2 =2

Q3: i dont get this one sry

4 0
2 years ago
5(k - 78) = 40<br> Please help
solong [7]

Answer:

k=86

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Help me plzzzzzzzzzz
ratelena [41]

Answer:

C

Step-by-step explanation:

im not 100% sure but i beleive its C

4 0
3 years ago
Billy walks 15 miles every day to soccer practice, and catches a ride home from his grandma. Billy had 5 practices last week. Ho
kirza4 [7]

Billy walked 75 yards last week

8 0
3 years ago
Write the equation –3x + 2y = 7 in slope-intercept form.
ira [324]
Y=mx+b is the slope formula

5 0
3 years ago
Other questions:
  • Having trouble with this question. Can someone help me.
    10·2 answers
  • The cost of 6 1/2 kg of apples is Rs. 520. What is the rate of one kg of apples
    6·1 answer
  • A buoy floating in the sea is bobbing in simple harmonic motion with period 2 seconds and amplitude 8 in. Its displacement d fro
    15·1 answer
  • please help! A student claims that a figure has rotational symmetry and that the angle of rotational symmetry is 360 degrees. Cr
    11·1 answer
  • 3 (3n-4)=3 (n+4) help help​
    10·1 answer
  • Which integer represents a loss of 11 yards in a football game?
    15·1 answer
  • What is the volume of a rectangular prism with the dimensions: base 2 3 /8 cm, height 1 1/3 cm, and length 3 3 /4 cm?
    5·2 answers
  • What is the value of f(-5) ?
    8·1 answer
  • Fill in the blank. Saber or Conocer??? please help me it's due tonight or else I get a zero.
    8·1 answer
  • I'm unsure on how to figure out what "X" is..?<br><br> X/2 = 6/3
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!