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defon
3 years ago
14

Which statement about the asymptotes is true with respect to the graph of this function?

Mathematics
2 answers:
Ratling [72]3 years ago
7 0
When you graph the equation you notice that there is 2 vertical and 1 horizontal asymptote. or D
tensa zangetsu [6.8K]3 years ago
3 0

Answer:

Option D.

Step-by-step explanation:

The given function is

f\left(x\right)=\dfrac{3x^{2}-3}{x^{2}-4}

In this function the degree of numerator an denominator is same i.e., 2.

Horizontal Asymptotes: If the degree of numerator an denominator is same, then

\text{Horizontal asymptote}=\frac{\text{Leading coefficient of numerator}}{\text{Leading coefficient of denominator}}

\text{Horizontal asymptote}=\frac{3}{1}

\text{Horizontal asymptote}=3

Horizontal asymptote is y=3.

f(x)=3

\dfrac{3x^{2}-3}{x^{2}-4}=3

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

x^{2}-1=x^{2}-4

1=4

This statement is false for any value of x, therefore the graph does not cross the horizontal asymtote.

Vertical Asymptotes: Equate the denominator equal to 0, to find the vertical asymptotes.

x^2-4=0

Add 4 on both sides.

x^2=4

Taking square root on both sides.

x=\pm \sqrt{4}

x=\pm 2

Vertical asymptotes are x=2 and x=-2.

The graph has two vertical asymptotes and one horizontal asymptote.

Therefore, the correct option is D.

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If f(x) = kx^3+ x^2 − kx + 2, find a number k such that the graph of f contains the point (k, -10)
Elina [12.6K]

If we write k where we see x in the equation and set the result equal to -10, we get the result.

  • f(k)=k(k)^3+k^2-k(k)+2
  • =k^4+k^2-k^2+2
  • =k^4+2=-10
  • k^4=-12
  • k_{1}=\sqrt[4]{3}(-1-i)
  • k_{2}=\sqrt[4]{3}(-1+i)
  • k_{3}=\sqrt[4]{3}(1-i)
  • k_{4}=\sqrt[4]{3}(1+i)

4 0
1 year ago
Social media is popular around the world. Statista provides estimate of the number of social media users in various countries in
amm1812

Answer:

Kindly check explanation

Step-by-step explanation:

The data table :

Use of SM _UK _China _ Russia _US _ col total

Yes ______480 __215 ___343 __640 _ 1678

No _______320 _ 285 ___357__ 360 _ 1322

Row Total__ 800 _500 __ 700_ 1000_ 3000

H0 : p1 = p2 = p3 = p4

H1 : p1 ≠ p2 ≠ p3 ≠ p4

Test statistic :

χ² = Σ(observed - Expected)² / Expected

Expected value of each cell = (Row total * column total) / N

N = grand total

Expected Values:

447.467 _279.667 _ 391.533 _ 559.333

352.533 _ 220.333 _ 308.467 _ 440.667

χ²=(2.36536+14.9527+6.01605+11.6337+3.00232 18.9793+7.63611+14.7665) = 79.352

Degree of freedom, df = (row-1)*(column-1) = (2 - 1) * (4 - 1) = 1 * 3 = 3

Using the Pvalue from Chisquare calculator :

Pvalue(79.352, 3) = 0.00000000001

Decision region :

Reject H0 ; If Pvalue < α

α = 0.05

Since 0.000000001 < 0.05 ; Reject H0 and conclude that not all population proportion are equal.

Sample proportion :

Phat = number of yes, x / total

For UK, Phat = 480/800 = 0.6

For China , Phat = 215/500 = 0.43

For Russia , Phat = 343/700 = 0.49

For US, Phat = 640/1000 = 0.64

7 0
3 years ago
Find four consecutive integers with the sum of -142
Akimi4 [234]

n, n + 1, n + 2, n + 3 - four consecutive integers

-142 - the sum

The equation:

n + (n + 1) + (n + 2) + (n + 3) = -142

n + n + 1 + n + 2 + n + 3 = -142

4n + 6 = -142     |subtract 6 from both sides

4n = -148    |divide both sides by 4

n = -37

n + 1 = -37 + 1 = -36

n + 2 = -37 + 2 = -35

n + 3 = -37 + 3 = -34

Answer: -37, -36, -35, -34.

5 0
3 years ago
Find the Least Common Denominator of the fractions: 6/7 and 2/3
serg [7]

Answer:

The least common denominator is 21

Step-by-step explanation:

3 & 7 equal 21 which is the least common factor that it equals

7 0
3 years ago
Read 2 more answers
Subtracting decimals
Fynjy0 [20]

Answer:

I am really good at doing stuff like that

5 0
3 years ago
Read 2 more answers
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