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max2010maxim [7]
3 years ago
14

let f(x)= p+ 8/x-q. the line x=4 is a vertical asymptote to the graph of f. what is the value of q and p, if the y intercept is

(0,4)?
Mathematics
1 answer:
svlad2 [7]3 years ago
7 0

Answer:

The value of q and p is 4 and -24  respectively.

Step-by-step explanation:

Being f(x)=\frac{p+8}{x-q} , the line x=4 is a vertical asymptote to the graph of f(x).  The line r is an asymptote of a function if the graph of the function is infinitely close to the line r. That is, an asymptote is a line to which a function approaches indefinitely, without ever touching it.

Being a rational function that which can be expressed as the quotient of two polynomials, a vertical asymptote occurs when the denominator is 0, that is, where the function is not defined. In this case:

x - q= 0

Solving:

x= q

Being the line x=4 the vertical asymptote, then

<u><em>4=q</em></u>

Then the function f (x) is:

f(x)=y=\frac{p+8}{x-4}

The y intercept is (0,4). This is, x= 0 and y=4. Replacing:

4=\frac{p+8}{0-4}

Solving:

4=\frac{p+8}{-4}

4*(-4)= p+8

-16= p+8

-16 - 8= p

<u><em>-24= p</em></u>

<u><em>The value of q and p is 4 and -24  respectively.</em></u>

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