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
Bogdan [553]
3 years ago
10

State the horizontal asymptote of the rational function.f(x) = quantity x squared plus six x minus eight divided by quantity x m

inus eight
Mathematics
2 answers:
padilas [110]3 years ago
4 0
F(x)=(x²+6x-8)/(x-8) has a vertical asymptote at x=8. When x is large f(x) approaches x which is a 45 degree line (gradient 1). There is no horizontal asymptote.
Alexus [3.1K]3 years ago
3 0

Answer:

There is no horizontal asymptote for the function f(x).

Step-by-step explanation:

We have the function f(x) = \frac{x^2+6x-8}{x-8}. Notice that if x=8 the function is not defined, because the denominator of the fractions equals zero, and the numerator don't. This fact is equivalent to the existence of a vertical asymptote at x=8. In mathematical language:

\lim_{x\rightarrow 8^+} \frac{x^2+6x-8}{x-8} = +\infty

and

\lim_{x\rightarrow 8^-} \frac{x^2+6x-8}{x-8} = -\infty.

Now, in case that f(x) has an horizontal asymptote the following must hold:

\lim_{x\rightarrow +\infty} \frac{x^2+6x-8}{x-8} = L\in\mathbb{R}

But, actually

\lim_{x\rightarrow \infty} \frac{x^2+6x-8}{x-8} = \infty.

Hence, there is no horizontal asymptote.

Anyway, f(x) has an asymptote, but no horizontal. In order to obtain the slope of the asymptote, we need to find the following limit:

\lim_{x\rightarrow +\infty} = \frac{f(x)}{x} = \lim_{x\rightarrow +\infty} \frac{x^2+6x-8}{x(x-8)} = \frac{x^2+6x-8}{x^2-8x} = 1.

Then asymptote has equation y=x+n. To find n we calculate the limit

\lim_{x\rightarrow +\infty} (f(x)-mx) = \lim_{x\rightarrow +\infty} \frac{x^2+6x-8}{x-8} -x = \lim_{x\rightarrow +\infty} \frac{14x-8}{x-8} = 14

Hence, the asymptote at +\infty is y = x+14.

You might be interested in
Calculate: <br><br> 462 grams(g)=____milligrams (mg)
egoroff_w [7]

Answer:

462 000mg

Step-by-step explanation:

1gram = 1000milligrams

Hence...462 grams...,

; 462 × 1000 = 462 000mg

3 0
3 years ago
If the distance from Haley’s house to school is 2.5 cm on the map and the actual distance is 3 miles. What is the scale for the
Brrunno [24]
To find your answer you divide 3 by 2.5 to get 1.2. The scale for the map is 1.2.

Hope this helps,
<em>♥Nikki♥</em>
(P.S. I'm not completely sure about this so you might want to get a second opinion on this particular question.)
7 0
3 years ago
How does changing the number outside the parentheses of an exponential function change your graph? y = a(b)^x
Zarrin [17]

Answer:

See Below.

Step-by-step explanation:

We have the function:

y=a(b)^x

Depending on the behavior of the coefficient, many things can happen. The parent exponential function has a=1. If a is something other than 1, however, there are three main changes.

Let’s use b=2 to illustrated the examples.

(In the graphed examples, below, the parent function (with b=2) is the red curve.)

  • If <em>a</em> is a positive, rational number greater than 1.

If a is a positive number other than 1, say 2, then this represents a vertical stretch.

In other words, our function is stretched closer to the y-axis.

(This is the blue curve. It is closer to the y-axis than the parent function (red curve).)

  • If <em>a</em> is a positive, rational number greater than 0 but less than 1.

If a is a number between 0 and 1 (so a fraction), say, 1/2, then this represents vertical compression.

In other words, our function gets farther away from the y-axis.

(This is the black curve.)

  • If <em>a </em>is a negative.

If a is <em>negative</em>, then this means that the graph was flipped over the x-axis.

(This is the green curve.)

Note that if we have something such as a=-2 or a=-1/2, this means that the function we flipped over the x-axis first and <em>then</em> vertically stretched or compressed.

(And example of this is illustrated with the orange curve).

3 0
3 years ago
Complex matching suggests that individuals who have formed a relationship may differ predominantly in the area of __________. A.
wlad13 [49]

Answer:

The answer is C. Physical attractiveness

Step-by-step explanation:

Physical attractiveness is a term describing the way people judge the physical appearances of others,

6 0
2 years ago
Pleassssss help me with the question thank you
Furkat [3]

The answer is 12

Blue eyes and brown eyes combined is 18 and the number of students with green eyes is 6

so 18 - 6 = 12

6 0
3 years ago
Other questions:
  • What is the value of x if 5x+2 = 59?
    6·2 answers
  • A cafeteria make 2,516 pounds of rice and 608 pounds of brown rice every month. after 6 months how many pounds of rice does the
    11·2 answers
  • 20.57 is 42.5% of ______.
    6·1 answer
  • The terms in the sequence decrease by the same amount each time:
    8·1 answer
  • Based only on the information given in the diagram, which congruence
    5·1 answer
  • Which of the following expressions results in 0 when evaluated at x = 4?
    7·1 answer
  • HELP!!<br><br> What is the area of this square, in square units?
    7·2 answers
  • If a car travels 55 miles per hour, how long will it have traveled if it travels 110 miles?
    14·2 answers
  • If k is the incenter of def find each measure
    10·1 answer
  • Find the velue of y? y²=169​
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!