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crimeas [40]
2 years ago
15

12) Write the equation of a rational function

Mathematics
1 answer:
aev [14]2 years ago
5 0

Answer:

\frac{4(x - 5)(x + 7)(x - 12)}{(x + 1)(x)(x - 12)}

Step-by-step explanation:

A rational function is

\frac{p(x)}{q(x)}

where q(x) doesn't equal zero.

If p is a asymptote, or hole at that value, then we will use

(x - p)

Step 1: We have asymptote as 0 and -1 so our denomiator will include

(x - 0)(x - ( - 1)

Which is

(x)(x + 1)

So our denomator so far is

\frac{p(x)}{x(x + 1)}

Step 2: Find Holes.

Since 12 is the value of the hole,

(x - 12)

is a the binomial.

This will be both on the numerator and denomator so qe have

\frac{(x - 12)}{x(x + 1)(x - 12)}

Step 3: Put the x intercepts in the numerator.

Since 5 and -7 is the intercepts,

\frac{(x - 12)(x - 5)(x + 7)}{x(x + 1)(x - 12)}

Step 4: Horinzontal Asymptotes,

Multiply the numerator and denomiator out fully,

\frac{  {x}^{3} - 10 {x}^{2}  - 59x + 420 }{ {x}^{3} - 12 {x}^{2}   + x - 12}

Take a L

look at the coefficients,

Notice they have the same degree,3, this means if we divide the leading coefficents, we will get our horinzonral asymptote.

Multiply the numerator by 4.

\frac{4(x - 12)(x - 5)(x - 7)}{x(x + 1)(x - 12)}

Above is the function,

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