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
Yuki888 [10]
3 years ago
13

Determine any asymptotes (Horizontal, vertical or oblique). Find holes, intercepts and state it's domain.

Mathematics
1 answer:
vesna_86 [32]3 years ago
8 0

Factorize the denominator:

\dfrac{x^2-4}{x^3+x^2-4x-4}=\dfrac{x^2-4}{x^2(x+1)-4(x+1)}=\dfrac{x^2-4}{(x^2-4)(x+1)}

If x\neq\pm2, we can cancel the factors of x^2-4, which makes x=-2 and x=2 removable discontinuities that appear as holes in the plot of g(x).

We're then left with

\dfrac1{x+1}

which is undefined when x=-1, so this is the site of a vertical asymptote.

As x gets arbitrarily large in magnitude, we find

\displaystyle\lim_{x\to-\infty}g(x)=\lim_{x\to+\infty}g(x)=0

since the degree of the denominator (3) is greater than the degree of the numerator (2). So y=0 is a horizontal asymptote.

Intercepts occur where g(x)=0 (x-intercepts) and the value of g(x) when x=0 (y-intercept). There are no x-intercepts because \dfrac1{x+1} is never 0. On the other hand,

g(0)=\dfrac{0-4}{0+0-0-4}=1

so there is one y-intercept at (0, 1).

The domain of g(x) is the set of values that x can take on for which g(x) exists. We've already shown that x can't be -2, 2, or -1, so the domain is the set

\{x\in\mathbb R\mid x\neq-2,x\neq-1,x\neq2\}

You might be interested in
Jacks family bought five concert tickets for $250 what was the price per ticket?
Mashcka [7]

answer : 0.02

$250 ÷ 5 = 0.02

5 0
2 years ago
Read 2 more answers
Need help finding slope, x-intercept, and y-intercept
butalik [34]

Step-by-step explanation:

count the slope, 5 up in 2.5 horizontal steps, slope = 5/2.5 or 2

x intercept is on the graph, 2.5

y intercept is also on the graph, -5

8 0
3 years ago
Read 2 more answers
The volume
Sedaia [141]
\bf \begin{array}{cccccclllll}
\textit{something}&&\textit{varies directly to}&&\textit{something else}\\ \quad \\
\textit{something}&=&{{ \textit{some value}}}&\cdot &\textit{something else}\\ \quad \\
y&=&{{ k}}&\cdot&x
&&  y={{ k }}x
\end{array}\\ \quad \\


and also

\bf \begin{array}{llllll}
\textit{something}&&\textit{varies inversely to}&\textit{something else}\\ \quad \\
\textit{something}&=&\cfrac{{{\textit{some value}}}}{}&\cfrac{}{\textit{something else}}\\ \quad \\
y&=&\cfrac{{{\textit{k}}}}{}&\cfrac{}{x}
&&y=\cfrac{{{  k}}}{x}
\end{array}


now, we know that V varies directly to T and inversely to P simultaneously
thus\bf V=T\cdot \cfrac{k}{P}

so     \bf V=T\cdot \cfrac{k}{P}\qquad 
\begin{cases}
V=42\\
T=84\\
P=8
\end{cases}\implies 42=\cfrac{84k}{8}\implies 4=k
\\\\\\
V=\cfrac{4T}{P}\qquad now\quad 
\begin{cases}
V=74\\
P=10
\end{cases}\implies 74=\cfrac{4T}{10}\implies 185=T
7 0
3 years ago
Determine whether each function represents exponential growth or decay
Karo-lina-s [1.5K]

Answer: Depends on the function but to figure this out you look for the growth factor in the equation is greater than 1

3 0
3 years ago
WIL GIVE BRAINLIEST ANSWER! HELP ASAP!
Evgesh-ka [11]

Answer:

Multiply the divisor and dividend by 100.

Step-by-step explanation:

The first step is to eliminate decimal points in both divisor and dividend. Since to convert 0.15 to a whole number you multiply by 100 then it means both the divisor and dividend should be multiplied by 100. So that we shall have 4860/15=324

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of the 5 in the number 356,409?​
    5·2 answers
  • At a local department store, jeans are typically priced at $15. Due to a special, the jeans are reduced to 80% of their original
    6·1 answer
  • Somebody please help me with the question
    12·1 answer
  • What is the smallest angle of rotational symmetry for a square
    15·2 answers
  • Suppose the equation of a line is 2x - 4y = - 8. Which coordinate pair represents the y-intercept?
    5·1 answer
  • Find the population mean or sample mean as indicated.<br> Sample: 17, 11, 8, 12, 22
    6·1 answer
  • Find the equation of the line through (0,-2) and (4, 18).
    6·1 answer
  • Use the root test to find the nature of the series : i need solutions details please
    13·1 answer
  • Solve for l:<br><img src="https://tex.z-dn.net/?f=v%20%3D%20%20%5Cfrac%7B%20%5Csqrt%7Bl%20%2B%20t%7D%20%7D%7B2%20%5Csqrt%7Bl%7D%
    14·1 answer
  • Just help me plz 10 pts
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!