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
Sav [38]
3 years ago
13

Find the vertical and horizontal asymptotes, domain, range, and roots of f (x) = -1 / x-3 +2.

Mathematics
1 answer:
gladu [14]3 years ago
5 0

Answer:

Vertical asymptote: x=3

Horizontal asymptote: f(x) =2

Domain of f(x) is all real numbers except 3.

Range of f(x) is all real numbers except 2.

Step-by-step explanation:

Given:

Function:

f (x) = -\dfrac{1 }{ x-3} +2

One root, x = 3.5

To find:

Vertical and horizontal asymptote, domain, range and roots of f(x).

Solution:

First of all, let us find the roots of f(x).

<em>Roots of f(x) means the value of x where f(x) = 0</em>

0= -\dfrac{1 }{ x-3} +2\\\Rightarrow 2= \dfrac{1 }{ x-3}\\\Rightarrow 2x-2 \times 3=1\\\Rightarrow 2x=7\\\Rightarrow x = 3.5

One root, x = 3.5

Domain of f(x) i.e. the values that we give as input to the function and there is a value of f(x) defined for it.

For x = 3, the value of f(x) \rightarrow \infty

For all, other values of x , f(x) is defined.

Hence, Domain of f(x) is all real numbers except 3.

Range of f(x) i.e. the values that are possible output of the function.

f(x) = 2 is not possible in this case because something is subtracted from 2. That something is \frac{1}{x-3}.

Hence, Range of f(x) is all real numbers except 2.

Vertical Asymptote is the value of x, where value of f(x) \rightarrow \infty.

-\dfrac{1 }{ x-3} +2 \rightarrow \infty

It is possible only when

x-3=0\\\Rightarrow x=3

\therefore vertical asymptote: x=3

Horizontal Asymptote is the value of f(x) , where value of x \rightarrow \infty.

x\rightarrow \infty \Rightarrow \dfrac{1 }{ x-3} \rightarrow 0\\\therefore f(x) =-0+2 \\\Rightarrow f(x) =2

\therefore Horizontal asymptote: f(x) =2

Please refer to the graph of given function as shown in the attached image.

You might be interested in
Two consecutive even integers have a sum of 34. find the integers​
poizon [28]

Answer: 16, 18

Step-by-step explanation:

16 + 18 = 34

3 0
3 years ago
2x+3y=1 and y=-2 - 9 solve using linear combination method. Please explain steps.
kaheart [24]

Answer:

x=17

Step-by-step explanation:

2x+3y=1

y=-2-9

  • In order to combine these two equations, an idea you need to keep in mind is finding a way of setting these equations as equal to each other. I saw that each equation shared a common value, y. In this case, we need to isolate y in the first equation so that both equations =y.

2x+3y=1

3y=-2x+1

\frac{3y}{3}=\frac{-2x+1}{3}

y=-\frac{2}{3}x+\frac{1}{3}

  • With this, we now know that both -2-9 and -\frac{2}{3}x+\frac{1}{3} are equal to y, so we can set them equal to each other.

y=-\frac{2}{3}x+\frac{1}{3}

y=-11

-\frac{2}{3}x+\frac{1}{3}=-11

  • Reply to this if anything I'm saying or doing is confusing in any way, or if you find a mistake. :) Solve for x.

-\frac{2}{3}x+\frac{1}{3}=-11

-\frac{2}{3}x=-11-\frac{1}{3}

-\frac{2}{3}x =-\frac{33}{3}-\frac{1}{3}

-\frac{2}{3}x =-\frac{34}{3}

-\frac{2}{3}x(-\frac{3}{2})=-\frac{34}{3}(-\frac{3}{2})

x=\frac{102}{6}=17

x=17

  • Hopefully this answer is correct AND makes sense in terms of how I achieved it. Again, reply to this with any questions or mistakes I made and I'll do my best to answer or fix them.

 

4 0
3 years ago
You can compare irrational numbers using rational approximation.
Natasha_Volkova [10]

Yes you can!!!!!!!!!!!

3 0
2 years ago
Jayde is wrapping a cube shape present that is 14 inches tall. How much wrapping paper will be needed to wrap the whole present?
gtnhenbr [62]

Answer:

1176in^2

Step-by-step explanation:

find the surface area of the cube

(14*14)6=1176 inches cubed

14*14 is finding the area of one side and then we multiply it by six because that's how many congruent sides there are

7 0
3 years ago
Read 2 more answers
All of the following equations have the same solution except _____. A. 7.5x = 1.5 B. x/5 = 0.04 C. x + 6.5 = 6.3 D. -1.8 + x = -
zysi [14]
I believe the answer is A. Hope I helped.
7 0
3 years ago
Read 2 more answers
Other questions:
  • For any positive numbers a, b, and d, with b. 1, logo(ag=
    11·1 answer
  • When full, a 22-gallon gas tank holds 129.8 pounds of gasoline. Estimate the weight of one gallon of gasoline. If it costs $91.3
    10·1 answer
  • According to some students, what is the true purpose of homework?
    5·1 answer
  • If the point (x, y) is in Quadrant III,<br> which of the following must be true?
    14·1 answer
  • You guy have any song requests?<br><br><br>​
    5·2 answers
  • Please help me, I need to pass this class
    9·1 answer
  • Please answer<br> *WILL GIVE BRAINLIEST*<br> DO NOT EXPLAIN
    14·1 answer
  • Hey! please help i’ll give brainliest
    13·2 answers
  • Please help with math problem give 5 star if do
    8·2 answers
  • What are the domain and range of the function mc013-1
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!