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MArishka [77]
3 years ago
15

Find the horizontal asymptote of the graph

Mathematics
2 answers:
sleet_krkn [62]3 years ago
5 0

y = -  \frac{1}{2}
alexgriva [62]3 years ago
4 0

Answer:

\frac{-1}{2}

Step-by-step explanation:

We are given that a fundtion

y=\frac{-4x^6+6x+3}{8x^6+9x+3}

We have to find the horizontal asymptote of the given function

We know that when degree of numerator and degree of denominator are equal then to get horizontal asymptote we divide the coefficient of heighest power of x in numerator by the coefficient of heighest power of x in denominator .

There are degree of both numerator and denominator are same .

Therefore, horizontal asymptote=\frac{-4}{8}

Horizontal asymptote=\frac{-1}{2}

Hence, the horizontal asymptote of given graph =\frac{-1}{2}

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m_a_m_a [10]
Ok, first you need to read a - g and mark down the information you know. Also, this continuous function can look pretty much like anything long as it has the a - g constraints/rule. 

A) We know the domain(x values) is between -10 to infinity
(-10,-9,-8,-7,-6,-5,-4,-3-,2,-1,0,1,2,3,4,5,6,7,8,9,10, to ---------> infinity)
B) We know the range(y values) is between -6 to infinity
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C) Next we know f(0) = f(4) = 0
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D) It tells us that f(x) (y) is increasing between the x values (-10,-6)  or (-2,2) or (4, to infinity)

E) It tells us that f(x) (y) is decreasing between the x values (-6,-2) or between (2,4)

F) Tells us that f(x) (y) is greater than or equal to between the x values of [-8,-4] or between the x values [0, to infinity) so this lets us know our drawing is going to be above or equal to 0 when we are in the values [-8,-4] or [0, to infinity)

G) Tells us that f(x) (y) is less than 0 when the function / drawing is between the x values of (-10, -8) or (-4,0)  

The picture is what the function could look like. It can be different but needs to following the rules that are given 




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