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1 year ago

What is the equation of the slant asymptote of the rational function?

Mathematics

1 answer:

marta [7]1 year ago

6 0

The equation of the slant asymptote of the rational function is; y = 2x - 3

<h3>What is the equation of the slant asymptote of the rational function?</h3>

We want to find the equation of the slant asymptote of the rational function given as;

f(x) = (10x³ - 15x² + x - 1)/(5x² - 2)

To solve this question, we will divide the numerator by the denominator. The result (not including the remainder) will be the equation of the slant asymptote.

We can tell the first term of the quotient will be 2x since 10x³/5x² = 2x. Thus, the answer from the given options will be either 2x − 3 or 2x − 11/5.

The easiest method to apply here is to simply multiply these options by the denominator to get;

(5x² − 2) (2x − 3) = 10x³ − 15x² − 4x + 6

(5x² − 2) (2x − 11/5) = 10x³ − 11x² − 4x + 22/5

So the answer must be 2x − 3

Thus, the equation of the slant asymptote of the rational function is; y = 2x - 3

Read more about Equation of Slant Asymptote at; brainly.com/question/17256965

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Help! I really need to pass!

Dmitriy789 [7]

Answer:

$\huge{ \boxed{ \bold{ \sf{y = - 2x + 6}}}}$

☥ $\tt{Question} :$

Write the equation of a line in slope - intercept form that has a slope of -2 and passes through the point ( - 1 , 8 ).

☥ $\tt{Step - \: by \: - \: step \: explanation}$

☪ $\underline{ \underline{ \text{Given : }}}$

Slope ( m ) = -2
Given point = ( - 1 , 8 )

☪ $\underline {\underline{ \text{To \: find}}} :$

Equation of a line in slope - intercept form ( i.e y = mx + c )

Let the point ( -1 , 8 ) be ( x₁ , y₁ )

☪ $\underline{ \underline{ \text{Solution}}} :$

$\underline{ \sf{y - y1 = m(x - x1)}}$

plug the known values :

↦ $\text{y - 8 = - 2 \{ x - ( - 1) \} }$

↦ $\text{y - 8 = - 2(x + 1)}$

Distribute -2 through the parentheses :

↦ $\text{y - 8 = - 2x - 2}$

Transpose 8 to right hand side and change it's sign

↦ $\text{y = - 2x - 2 + 8}$

↦ $\boxed{ \text{y = - 2x + 6}}$

And we're done !

Hope I helped!

♡ Have a wonderful day / night ツ

~TheAnimeGirl ♪

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