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vampirchik [111]
2 years ago
9

Let f(x)= x(2x-3)/(x+2)x. Find the domain, vertical and horizontal asymptote

Mathematics
1 answer:
Reptile [31]2 years ago
7 0

Step-by-step explanation:

Domain of a rational function is everywhere except where we set vertical asymptotes. or removable discontinues

Here, we have

\frac{x(2x - 3)}{(x + 2)x}

First, notice we have x in both the numerator and denomiator so we have a removable discounties at x.

Since, we don't want x to be 0,

We have a removable discontinuity at x=0

Now, we have

\frac{2x - 3}{x + 2}

We don't want the denomiator be zero because we can't divide by zero.

so

x + 2 = 0

x =  - 2

So our domain is

All Real Numbers except-2 and 0.

The vertical asymptors is x=-2.

To find the horinzontal asymptote, notice how the numerator and denomator have the same degree. So this mean we will have a horinzontal asymptoe of

The leading coeffixent of the numerator/ the leading coefficent of the denomiator.

So that becomes

\frac{2}{1}  = 2

So we have a horinzontal asymptofe of 2

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Lady_Fox [76]

Answer:

y = \frac{4}{3} x + \frac{41}{3}

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y-intercept )

here m = \frac{4}{3}, hence

y = \frac{4}{3} x + c ← is the partial equation

to find c substitute (- 2, 11) into the partial equation

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aleksandr82 [10.1K]

Answer:

An airline claims that the no-show rate for passengers is less than 5%. In a sample of 420 randomly selected reservations, 19 were no-shows. At α=0.01, test the airline's claim. State the sample percentage and round it to three decimal places.

State the hypotheses.

State the critical value(s).

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Answer:

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