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Colt1911 [192]
3 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]3 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.

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lubasha [3.4K]

Answer:

Sometimes I l i c k  myself like a cat but other times I'll just get orange juice and pour it on myself. Either way works great!

Step-by-step explanation:

8 0
3 years ago
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In a regression equation predicting income (measured in $1000s) with education (measured in years), the intercept (a) equals 1.5
Sindrei [870]

Answer:

a. at zero years of education, income equals $1500

Step-by-step explanation:

The equation for income 'I', as a function of years of education 't' is given by:

i(t) = bt+a

Where b is the regression coefficient and a is the intercept.

The intercept is the value assumed by the function for t = 0 years of education:

i(0) = 0*4 +1.5\\i(0) = 1.5

Since the income function measures income in $1,000s, at zero years of education, income equals $1500

3 0
3 years ago
Suppose the population of a certain city is 5289 thousand. It is expected to decrease to 4530 thousand in 50 years. Find the per
Tcecarenko [31]

Answer:

14.4% decrease

Step-by-step explanation:

Here is the formula for finding the percentage of decrease:

(starting value - final value) / starting value * 100.

So for your question,

\frac{5289-4530}{5289} =.0144\\.0144 * 100 = 14.4\\/

There was a 14.4% decrease within 50 years.

5 0
3 years ago
Which graph represents the function y = cos(4x)?<br><br> Answer is graph B
VARVARA [1.3K]

Answer:

Step-by-step explanation:

Let the equation of the cosine function is,

y = Acos(Bx)

From the graph attached,

A = Amplitude = \frac{1-(-1)}{2}

   = 1

B = \frac{2\pi}{\text{Period}}

B = \frac{2\pi}{\frac{\pi}{2}-0}

B = \frac{4\pi}{\pi}

B = 4

Therefore, equation of the cosine wave given in the graph will be,

y = 1.Cos(4x)

y = Cos(4x)

7 0
3 years ago
Read 2 more answers
1.
nikdorinn [45]

Answer:

C. 28 = (2x - 1)(x)

Step-by-step explanation:

There is a rectangular swimming pool.

Width of swimming pool is x  

Length is  one less than twice the width

Area of the swimming pool is  28 sq ft.

To Find : Equation could be used to model the area of the swimming pool.

Solution:  

Since we are given that Length is one less than twice the width.

And width is x (given)

So, length = 2x-1

Area of the swimming pool is  28 sq ft.

Now ,

Formula of area of rectangle : Length*Width

⇒28= (2x-1)(x)

So,  equation used to model the area of the swimming pool: 28= (2x-1)(x)

Hence Option c is correct.

3 0
3 years ago
Read 2 more answers
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