PLEASE HELP ME HAVGDJSGEVSJSGE

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

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

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 owner of a new pet store wishes to display tropical fish in display tanks. The above table shows the species that cannot liv

Pepsi [2]

Answer:

The minimum number of different tanks needed to safely house all the fish is:

3 tanks.

Step-by-step explanation:

To identify the minimum number of different tanks, we're gonna concentrate in a fish species, in this case can be the A: as you see in the table, the A species can live with all the fish excepting the F and G, by their side, the F and G can't live together , by this reason, this three species must live in a different tank, in the next form:

Tank 1: A
Tank 2: F
Tank 3: G

Now the B species, it can live with A, F and G, but for this example we can put in the tank 1 (the tank of the A species). The C especies can live with A, F and G, but how we have A and B together, we're gonna put the C especies in the tank 3 (the tank of the G especies). The D species can live with A and G, we're gonna put in the tank 1 because can live with B species too. The E species can live with A and F, we're gonna put in the tank 2 (the tank of the F species) because the E species can't live with D that is in the in the tank 1. Al last, the H species just can live with A, E, F, and H species, by this reason, the only tank that can be put is the tank 2. In this form, the order is the next:

Tank 1: A, B, D.
Tank 2: F, E, H.
Tank 3: G, C.

And the owner of the pet store must buy three different tanks to display these tropical fish.

5 0

3 years ago

Javier asks his mother how old a tree in their yard is. His mother says, “The sum of 10 and two-thirds of that tree’s age, in ye

Vaselesa [24]

Answer:

Javier's equation is not correct because the variable "a" should be multiplied by only and then added to

Step-by-step explanation:

Let

a------>is the tree’s age in years

we have that

-------> Javier's equation

we know that

The equation that represent the situation is equal to

Solve for a

Multiply by both sides

Javier's equation is not correct because the variable "a" should be multiplied by only and then added to

6 0

3 years ago

Read 2 more answers

The price of a game that’s been discounted 18% OFF ITS list price (x)

marta [7]

First you convert the percentage into a decimal. 18% to 0.18, then you multiply that decimal to the price of the item being discounted and bam, you have your price.

7 0

3 years ago

I need help with this math thing thanks

pshichka [43]

See attached picture for answer

3 0

3 years ago

Read 2 more answers