Answer:
The value of q and p is 4 and -24 respectively.
Step-by-step explanation:
Being
, 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}](https://tex.z-dn.net/?f=f%28x%29%3Dy%3D%5Cfrac%7Bp%2B8%7D%7Bx-4%7D)
The y intercept is (0,4). This is, x= 0 and y=4. Replacing:
![4=\frac{p+8}{0-4}](https://tex.z-dn.net/?f=4%3D%5Cfrac%7Bp%2B8%7D%7B0-4%7D)
Solving:
![4=\frac{p+8}{-4}](https://tex.z-dn.net/?f=4%3D%5Cfrac%7Bp%2B8%7D%7B-4%7D)
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>