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Grace [21]
3 years ago
10

What is the oblique asymptote of the function f(x) = the quantity x squared minus 5x plus 6 over the quantity x minus 4?

Mathematics
1 answer:
Paraphin [41]3 years ago
4 0

Answer:

x - 1

Step-by-step explanation:

We know that, a slant or oblique asymptote of a rational function is the asymptote that helps in determining the direction of the function.

It occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator.

Now, we divide the numerator by denominator using long division method and the first two terms in the quotient ( forming a linear function ) is the equation of the oblique asymptote.

We are given the rational function, f(x) = \frac{x^{2}-5x+6}{x-4}.

After dividing we get that, the quotient is x - 1.

Hence, the equation of the oblique asymptote is x-1.

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What is the average rate of change of the function over the interval x = 0 to x = 6?
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15 2/3, or 47/3

Step-by-step explanation:

I'm going to assume, correctly or not, that you actually meant f(x) = 2x^2 - (1/3)x + 5.  Double check on this right now, please.

If I'm right, then evaluate f(x) at x = 0 and x = 8:

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Then the average rate of change of f(x) = 2x^2 - (1/3)x + 5 over the interval [0,8] is:

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a. r. c. = ------------------- = ---------------- = 15 2/3, or 47/3

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