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
Colt1911 [192]
2 years ago
10

20%7D" id="TexFormula1" title="f(x) - \frac{x^{2}-4 }{x^{4} +x^{3} -4x^{2}-4 }" alt="f(x) - \frac{x^{2}-4 }{x^{4} +x^{3} -4x^{2}-4 }" align="absmiddle" class="latex-formula">
What is the:

Domain:

V.A:

RootsL

Y-Int:

H.A:

Holes:

O.A:


Also, graph it.

Mathematics
1 answer:
Llana [10]2 years ago
6 0

a) The given function is

f(x)=\frac{x^2-4}{x^4+x^3-4x^2-4}

The domain refers to all values of x for which the function is defined.

The function is defined for

x^4+x^3-4x^2-4\ne0

This implies that;

x\ne -2.69,x\ne 1.83

b) The vertical asymptotes are x-values that makes the function undefined.

To find the vertical asymptote, equate the denominator to zero and solve for x.

x^4+x^3-4x^2-4=0

This implies that;

x= -2.69,x=1.83

c) The roots are the x-intercepts of the graph.

To find the roots, we equate the function to zero and solve for x.

\frac{x^2-4}{x^4+x^3-4x^2-4}=0

\Rightarrow x^2-4=0

x^2=4

x=\pm \sqrt{4}

x=\pm2

The roots are x=-2,x=2

d) The y-intercept is where the graph touches the y-axis.

To find the y-inter, we substitute;

x=0 into the function

f(0)=\frac{0^2-4}{0^4+0^3-4(0)^2-4}

f(0)=\frac{-4}{-4}=1

e) to find the horizontal asypmtote, we take limit to infinity

lim_{x\to \infty}\frac{x^2-4}{x^4+x^3-4x^2-4}=0

The horizontal asymtote is y=0

f) The greatest common divisor of both the numerator and the denominator is 1.

There is no common factor of the numerator and the denominator which is  at least a linear factor.

Therefore the function has no holes.

g) The given function is a proper rational function.

There is no oblique asymptote.

See attachment for graph.

You might be interested in
Which polynomial expression represents the area of the outer most square tile, shown below?
Andrew [12]

ANSWER

{x}^{2}  - 6x + 9

EXPLANATION

The outermost square tile has side length,

l = x - 3

The area of a square is given by;

Area= {l}^{2}

We substitite the given expression for the side length into the formula to obtain,

Area= {(x - 3)}^{2}

Area= {(x - 3)}(x - 3)

We expand using the distributive property to obtain;

Area=x {(x - 3)} - 3(x - 3)

This gives us:

Area= {x}^{2}  - 3x - 3x  + 9

Area= {x}^{2}  - 6x + 9

The last choice is correct.

7 0
3 years ago
Read 2 more answers
PLEASE I REALLY NEED HELP PLEASE!!!!!!
DochEvi [55]

I think that can help for now

7 0
3 years ago
I don't know how to do this. Any help?
Brut [27]

Answer:

cos 37=x/b (second one)

sin 37= a/b (third one)

tan 37=a/x (sixth one)

Step-by-step explanation:

Cos is defined by the adjacent side over the hypotenuse. Cos 37 would be x/b. Clearly, that is option 2. Sin is defined by opposite over hypotenuse. Sin 37 would be a/b. That is the 3rd option. Tan is defined by opposite over adjacent. Tan 37 would be a/x or the 6th option.

7 0
3 years ago
1. How many real solutions does the quadratic equation x?+9x= -8 have?​
likoan [24]

Answer:

This quadratic equation has 2 solutions.

Step-by-step explanation:

I assume the '?' in your question is meant to be power 2 (²), or else it would not be a quadratic equation. You could write it using the superscript version of 2.

We can solve this equation by expressing it in the form: ax² + bx + c

x² + 9x= -8

x² + 9x + 8 = 0

Now if you know the discriminant, you can simply plug in your values of a, b, and c to see how many solutions there are.

In this case, you would not need the discriminant as there are whole-number factors and hence this can simply be factorised.

x² + 9x + 8 = 0

(x + 8)(x + 1) = 0

For this equation to be true (= 0), x can equal -8 OR -1.

Hence, this quadratic equation has 2 solutions.

5 0
2 years ago
How much interest will be earned on a $6,000 investment at 2.25% for 5 years. Round to the
Monica [59]

Final amount = 6675, interest earned will be 675

3 0
3 years ago
Other questions:
  • What is positive 0.833 repeating as a fraction
    5·1 answer
  • What is the product?
    9·2 answers
  • How do you find the exact surface area of a rectangular <br> prism?
    12·1 answer
  • Ahmed and Karnia are building scenery of the Egyptian pyramids out of plywood for a community play. They pyramids are represente
    14·1 answer
  • The Sommers family planted a new flower garden. 20% of the flowers are yellow, 15% of the flowers are purple, 40% of the flowers
    7·1 answer
  • Solve the inequality of t/4 &gt; 6
    6·1 answer
  • What is the most specific description of ABCD?
    13·1 answer
  • How did you compute the cost of 4 pounds of beef at $5.89 per pound? Use this example to explain your strategy.
    5·1 answer
  • What is the surface area of the cylinder with height 5 mi and radius 2 mi? Round your
    10·1 answer
  • New ear buds cost $48. There is a 10% discount. What is the new cost?
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!