All categories

2 years ago

What are the vertical and horizontal asymptotes for the function f(x)=x^2+x-6/x^3-1?

Mathematics

2 answers:

ch4aika [34]2 years ago

8 0

Answer:

Step-by-step explanation:

For clarity, f(x)=x^2+x-6/x^3-1 should be written as:

x^2 + x - 6

f(x) = ------------------

x^3 - 1

Note that the denominator, x^3 - 1, factors as follows: (x - 1)(x^2 + x + 1). If we set these results = to 0 individually, we find that there is only one real root; it is x = 1. We cannot divide by zero, so conclude that the given function is undefined at x = 1. Thus, the function has the vertical asymptote x = 1.

Note that x^2 in the numerator is of a higher power than is x^3 in the denominator. As x grows large without bound, either + or - , this ratio x^2/x^3 approaches zero. Thus, the horizontal asymptote is y = 0.

The correct answer choice is (b).

saveliy_v [14]2 years ago

7 0

Answer:

its b

Step-by-step explanation:

You might be interested in

Point A is at (3, -8) and point B is at (7, 3). What is the midpoint of line segment AB?

allochka39001 [22]

Answer:

$(5, -5/2)$

Step-by-step explanation:

The midpoint of any line segment is the average of the x- and y-values of the two endpoints.

Therefore, the midpoint of $AB$ is $((3+7)/2, (-8+3)/2)=(10/2, -5/2)=(5, -5/2)$ .

So, the answer is $\boxed{(5, -5/2)}$ and we're done!

5 0

2 years ago

I have a box of 24 different types of cup cakes. 1⁄2 of the cupcakes are vanilla. 1⁄8 of the cupcakes are strawberry. And the re

AlexFokin [52]

Answer:

21 7/8 is choclate

1/2 or 2 is vanilla

1/8 is strawberry

Step-by-step explanation:

1/2 x 4 is is 2

1/8 < 2

2 of the cupcakes (into eights) are vanilla from which a dominatorof 8

2 plus 1/8 is 2 1/8

24 - 2 1/8 is 21 7/8

8 0

2 years ago

A group of college students developed a solar-powered car and entered it in a race. The car travels at a constant speed of 100 m

nekit [7.7K]

Answer:

A) Distance time graph

B) d(t) = 25t

C) The expression shows the distance more clearly.

Step-by-step explanation:

A) A distance time graph as seen in the attachment provides a representation of the distance travelled.

We are told the car travels at a constant speed of 100 meters per 4 seconds. Which means that 100 m for each 4 hours. So, for 200m, it's 8 hours like seen in the graph and for 300m,it's 12 hours as seen in the graph.

B) And expression for the distance is;

d = vt

Where;

d is distance in metres

v is speed in m/s and t is time

We are told that the car travels at a constant speed of 100 meters per 4 seconds.

Thus, v = 100/4 = 25 m/s

Distance travelled over time is;

d(t) = 25t

C) Looking at both A and B above, it's obvious that the expression of the distance shows a more clearer way of getting the distance because once we know the time travelled, we will just plug it into the equation and get the distance. Whereas, for the representation form, one will need to longer graphs if the time spent is very long.