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3 years ago

Find the vertical and horizontal asymptote if they exist

Mathematics

1 answer:

tresset_1 [31]3 years ago

7 0

Hello!

Vertical asymptotes are determined by setting the denominator of a rational function to zero and then by solving for x.

Horizontal asymptotes are determined by:

1. If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

2. If the degree of the numerator = degree of denominator, then y = leading coefficient of numerator / leading coefficient of denominator is the horizontal asymptote.

3. If degree of numerator > degree of denominator, then there is an oblique asymptote, but no horizontal asymptote.

To find the vertical asymptote:

2x² - 10 = 0

2(x² - 5) = 0

(x - √5)(x + √5) = 0

x = √5 and x = -√5

Graphing the equation, we realize that x = -√5 is not a vertical asymptote, so therefore, the only vertical asymptote is x = √5.

To find the horizontal asymptote:

If the degree of the numerator < degree of denominator, then the line, y = 0 is the horizontal asymptote.

Therefore, the horizontal asymptote of this function is y = 0.

Short answer: Vertical asymptote: x = √5 and horizontal asymptote: y = 0

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3 years ago

A rectangular vegetable garden will have a width that is 4 feet less than the length, and an area of 140 square feet. If x repre

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Answer:

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Step-by-step explanation:

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replacing'

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2 years ago

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3 years ago

For every 6 kg of a child's weight, pediatricians prescribe 7 mg of fever reducer. If Greg weighs 42 kg, how many milligrams

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Answer:

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3 years ago

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10 - x = 2(-2x - 4) Identify with either No Solution or All Real Numbers.

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Answer:

$\Huge\boxed{\mathsf{\Rightarrow X=-6}}}$

Step-by-step explanation:

Isolate x on one side of the equation.

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⇒ A(B-C)=AB-AC

A=2

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C=4

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Rewrite the equation problem.

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Solve.

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3x=-18 (Solve.)

3x/3=-18/3 (Divide by 3 from both sides.)

-18/3 (Solve & Simplify.)

-18/3=-6

X=-6

$\Large\boxed{\mathsf{X=-6}}}$

Therefore, the correct answer is x=-6.

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