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
Shtirlitz [24]
3 years ago
8

Given the functionf ( x ) = x^2 + 7 x + 10/ x^2 + 9 x + 20

Mathematics
1 answer:
vladimir1956 [14]3 years ago
5 0

<em>x = -4 is a vertical asymptote for the function.</em>

<h2>Explanation:</h2>

The graph of y=f(x) is a vertical has an asymptote at x=a if at least one of the following statements is true:

1) \ \underset{x\rightarrow a^{-}}{lim}f(x)=\infty\\ \\ 2) \ \underset{x\rightarrow a^{-}}{lim}f(x)=-\infty \\ \\ 3) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty \\ \\ 4) \ \underset{x\rightarrow a^{+}}{lim}f(x)=\infty

The function is:

f(x)=\frac{x^2+7x+10}{x^2+9x+20}

First of all, let't factor out:

f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20} \\ \\ f(x)=\frac{x(x+5)+2(x+5)}{x(x+5)+4(x+5)} \\ \\ f(x)=\frac{(x+5)(x+2)}{(x+5)(x+4)} \\ \\ f(x)=\frac{(x+2)}{(x+4)}, \ x\neq  5

From here:

\bullet \ When \ x \ approaches \ -4 \ on \ the \ right: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(-4^{+}+2)}{(-4^{+}+4)} \\ \\ \\ The \ numerator \ is \ negative \ and \ the \ denominator \\ is \ a \ small \ positive \ number. \ So: \\ \\ \underset{x\rightarrow -4^{+}}{lim}\frac{(x+2)}{(x+4)}=-\infty

\bullet \ When \ x \ approaches \ -4 \ on \ the \ left: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=? \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(-4^{-}+2)}{(-4^{-}+4)} \\ \\ \\ The \ numerator \ is \ a \ negative \ and \ the \ denominator \\ is \ a \ small \ negative \ number \ too. \ So: \\ \\ \underset{x\rightarrow -4^{-}}{lim}\frac{(x+2)}{(x+4)}=+\infty

Accordingly:

x=-4 \ is \ a \ vertical \ asymptote \ for \\ \\ f(x)=\frac{x^2+5x+2x+10}{x^2+5x+4x+20}

<h2>Learn more:</h2>

Vertical and horizontal asymptotes: brainly.com/question/10254973

#LearnWithBrainly

You might be interested in
Evaluate 5+x-5*8 for x = 7
Sladkaya [172]

Answer:

- 28

Step-by-step explanation:

Plug in 7 for x

5 + 7 - 5 x 8

5 + 7 - 40

12 - 40

-28

8 0
3 years ago
A recipe requires
Alla [95]

Answer:

22/3=8/3=2.66

if 12 servings =2.6 cup of flour

...18 servings=???????

18×2.6/12=3.9

the answer is 3.9

6 0
2 years ago
NEED HELP ASAP WILL GIVE BRAINLIEST REAL ANSWERS ONLY PLZ REPORT LINKS OR PEOPLE ANSWERING FOR POINTS
nikklg [1K]

Answer:

B

Step-by-step explanation:

Trust

6 0
2 years ago
ADante begins to evaluate the expression 3 1/3 × 51/4 using the steps below. Which could be his next step?
antiseptic1488 [7]

Answer:

31/3 ×51/4

527/4

Step-by-step explanation:

4 0
3 years ago
The circumference of a circle is 37.68 meters. What is the area of the circle?
german
The area of the circle is <span>112.98 m squared</span>
4 0
3 years ago
Other questions:
  • Another way to 7x+4(x+5)
    7·1 answer
  • Find the area of the trapezoids
    6·1 answer
  • Determine the two positive integers the the square root of 7 fall in between. (write the word "and" in between your answer
    13·1 answer
  • The ratio of boys to girls in the checker club at Anastasia school is equal to 2:3 the number of club members is more than 20 an
    7·1 answer
  • What is 61 ones times1/10
    7·2 answers
  • Samantha conjectures that for x &lt; -1, it is true that x5 - 2 &gt; x. Is her conjecture correct? Why or why not?
    12·1 answer
  • How do you work out 8 something 2 something 1 =24 ?
    9·2 answers
  • Complete the sentence the length of a segment from a vertex to the centroid is the length of the median from that vertex
    13·1 answer
  • a sixth grade student can complete 20 multiplication facts in one minute if you works at the same rate how long should it take h
    8·2 answers
  • The school store sells Midville High T-shirts for $12 each and Midville High gym shorts for $9 a pair. One afternoon they sold a
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!