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3 years ago

Determine the equations of the vertical and horizontal asymptotes, if any, for f(x) =2x/x+4

Mathematics

1 answer:

Tamiku [17]3 years ago

8 0

Option C: $x=-4$ , $y=2$ is the asymptotes of the equation.

Explanation:

The equation is $f(x)=\frac{2x}{x+4}$

The vertical asymptote of the equation can be determined by equating the denominator of the equation to zero.

Thus, we have,

$x+4=0$

$x=-4$

Hence, the vertical asymptote of the function is $x=-4$

Now, we shall determine the horizontal asymptote.

The horizontal asymptote of the function can be determined by dividing the leading coefficient of x in the numerator by the leading coefficient of x in the denominator.

Thus, we have,

$y=\frac{2}{1}$

$y=2$

Hence, the horizontal asymptote of the function is $y=2$

Therefore, Option C is the correct answer.

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3 years ago

Find a polynomial of the form

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Answer:

$f(x)=-\frac{1}{4}x^3-\frac{1}{6}x^2+\frac{65}{12}x-3$

Step-by-step explanation:

We are given that

$f(x)=ax^3+bx^2+cx+d$

f(0)=-3,f(1)=2,f(3)=5 and f(4)=0

We have to find the polynomial

Substitute the value x=0 then ,we get

f(0)=d=-3

Substitute x=1 then we get

$a+b+c-3=2$

$a+b+c=2+3=5$

$a+b+c=5$ (equation I)

Substitute x=3 then we get

$a(3)^3+b(3)^2+c(3)-3=5$

$27a+9b+3c=5+3=8$

$27a+9b+3c=8$ (Equation II)

Substitute x=4 then we get

$a(4)^3+b(4)^2+c(4)-3=0$

$64a+16b+4c=3$ (Equation III)

Equation I multiply by 3 then subtract from equation II

$24a+6b=-7$ (Equation IV)

Equation II multiply by 4 and equation III multiply by 3 and subtract equation II from III

$84a+12b=-23$ (Equation V)

Equation IV multiply by 2 and then subtract from equation V

$36a=-9$

$a=-\frac{9}{36}$

$a=-\frac{1}{4}$

Substitute the value of a in equation IV then we get

$24(-\frac{1}{4})+6b=-7$

$-6+6b=-7$

$6b=-7+6=-1$

$b=-\frac{1}{6}$

Substitute the value of b in equation I then we get

$-\frac{1}{4}-\frac{1}{6}+ c=5$

$-\frac{5}{12}+c=5$

$c=5+\frac{5}{12}=\frac{65}{12}$

Substitute the values then we get

$f(x)=-\frac{1}{4}x^3-\frac{1}{6}x^2+\frac{65}{12}x-3$

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4 years ago

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Answer:

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Step-by-step explanation:

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3 years ago

Help: A marching band is rehearsing. 4/5 of the marching band members play percussion instruments. 4/6 of the percussionists pla

GaryK [48]

Answer: 1.2/5 Marching band members play the snare drum.

Step-by-step explanation:

4/5 Band Members Play Percussion Instruments. (80%)

4/6 Play The Snare Drum. (66% of the 80%)

1/5 Band Members Do NOT play percussion. (20%)

80 - 66 = 14%

14 + 20 = 24%

1/5 = 20%

1.5/5 = 30%

1.2/5 = 24%

1.2/5 Marching band members play the snare drum.

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3 years ago

WILL MARK BRAINIEST!! 50 POINTS.

galben [10]

Answer:

Part A: The two types of types of transformation are

1) Rotation of 11.3° about (1, 2)

2) By algebraic transformation

Part B:

Rotation by 11.3° and T(2 - y)×1/2 + x, 0)

Part C: The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)

Step-by-step explanation:

The coordinates through which the linear function f(x) passes = (1. 3) and (3, 13)

The coordinates through which the linear function g(x) passes = (1, 3) and (1, 13)

The equation for f(x) in slope and intercept form. y = m·x + c is given as follows;

The slope, m = (13 - 3)/(3 - 1) = 5

The equation in point and slope form is y - 3 = 5×(x -1)

y = 5·x - 5 + 3 = 5·x - 3

y = 5·x - 3

The equation for g(x) in slope and intercept form. y = m·x + c is given as follows;

The slope, m = (13 - 3)/(1 - 1) = ∞

∴ The equation in point and slope form is x = 1

Therefore, the two equations meet at the point (1, 2)

The transformation that can be used to transform f(x) to g(x) is T(2 - y)×1/2 + x, 0)

2) Another transformation that can be used is to rotate f(x) by the vertex angle as follows

Vertex angle is 90° - tan⁻¹(m) = 90° - tan⁻¹(5) ≈ 11.3°

Rotation of f(x) by 11.3° about (1, 2) gives g(x)

Hope this helped!

7 0

2 years ago

Read 2 more answers