PLEASE HELP! AS SOON AS POSSIBLE I HAVE TO BE DONE IN 10 MINS !

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

insens350 [35]

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

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

6 0

3 years ago

The ratio of apples to orgens is 1 to 3

-BARSIC- [3]

Because the ratio is 1 to 3. It means that For every one apple there are 3 oranges. So If there are 2 apples, there would n 6 oranges. If there are twelve apples, there would be 36 oranges. To find the number of oranges for the amount of apples, just multiply the number of apples by 3.

8 0

4 years ago

What is 52/6 in simplest form

zimovet [89]

52/6 in simplest form is 8 2/3 I got the answer 8 2/3 because 6 can go into 52 8 times and there is a remainder the remainder that I got was 4 . I'll put the remainder over the denominator which is 6. So right now I would have 8 4/6 but this fraction can be simplied again by 2 so the final answer is 8 2/3

3 0

3 years ago

Read 2 more answers

Samuel and Zander together have $392. Samuel has six times as much money as Zander. How much does each have? Please help! Quick

Shalnov [3]

Answer:

Samuel has $336 and Zander has $56

Step-by-step explanation:

Samuel = 6x because he has 6 times Zander

Zander = x

Together they have 392

6x + x = 392

7x = 392

Divide both sides by 7

x = 56

Samuel = 6 x 56 = 336

Zander = 56

336 + 56 = 392

3 0

3 years ago

A relationship between two variables is described below. We can think of one variable as helping to explain the other. Is the in

kramer

Answer:

Explanatory Variable

Step-by-step explanation:

The variable that we can change is called the Explanatory variable.

The response variable dependent upon the explanatory variable, as we change the value of the explanatory variable the value of the response variable is also gets changed.

The number of years smoking a cigarette is in our control so it is an explanatory variable.

and, the impact of the number of years smoking a cigarette is directly on lung capacity, so it is Response variable.

3 0

4 years ago