Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the vertical and horizontal asymptotes of the function:

f(x)=((2x-1)(3x+1))/((x-2)(x+4))
The fields below accept a list of numbers or formulas separated by semicolons (e.g.
2;4;6 or
x+1;x-1). The order of the list does not matter.
Vertical asymptotes:

x=
Horizontal asymptotes:

y=

◻

$\newline$ Find the vertical and horizontal asymptotes of the function: $\newline$ $f(x)=\frac{(2 x-1)(3 x+1)}{(x-2)(x+4)}$ $\newline$ The fields below accept a list of numbers or formulas separated by semicolons (e.g. $2 ; 4 ; 6$ or $x+1 ; x-1)$ . The order of the list does not matter. $\newline$ Vertical asymptotes: $\newline$ $x=$ $\newline$ Horizontal asymptotes: $\newline$ $y=$ $\newline$

View step-by-step help

View step-by-step help

Full solution

Q.

\newline

Find the vertical and horizontal asymptotes of the function:

\newline

f(x)=\frac{(2 x-1)(3 x+1)}{(x-2)(x+4)}

\newline

The fields below accept a list of numbers or formulas separated by semicolons (e.g.

2 ; 4 ; 6

or

x+1 ; x-1)

. The order of the list does not matter.

\newline

Vertical asymptotes:

\newline

x=

\newline

Horizontal asymptotes:

\newline

y=

\newline

Find Vertical Asymptotes: To find the vertical asymptotes, set the denominator equal to zero and solve for $x$ . $(x-2)(x+4) = 0$ $x-2 = 0 \text{ or } x+4 = 0$ $x = 2 \text{ or } x = -4$
Compare Degrees for Horizontal Asymptotes: For the horizontal asymptotes, compare the degrees of the numerator and the denominator. $\newline$ Degree of numerator $(2x-1)(3x+1) = 2$ (since it's a product of two first-degree polynomials). $\newline$ Degree of denominator $(x-2)(x+4) = 2$ (same reason as above).
Calculate Horizontal Asymptote: Since the degrees are the same, the horizontal asymptote is found by dividing the leading coefficients of the numerator and the denominator. $\newline$ Leading coefficient of numerator = $2 \times 3 = 6$ $\newline$ Leading coefficient of denominator = $1 \times 1 = 1$ $\newline$ Horizontal asymptote: $y = \frac{6}{1} = 6$

More problems from Power rule

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 9 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 5 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 5 months ago

Question

\newline

32^{(-1/5)}

Posted 7 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 8 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 7 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant