Question

122
course
ap precalculus
due tue, sep 23, 2025
12
default gallery

1. give the equation of a transformation of a basic function that has an asymptote at x = 4 and a key point at the (6,9)

Explanation:

Step1: Consider a rational - type function

A rational function of the form $y=\frac{a}{x - h}+k$ has a vertical asymptote at $x = h$. Given the asymptote $x = 4$, we have $h = 4$, so the function is $y=\frac{a}{x - 4}+k$.

Step2: Substitute the key - point

Substitute the point $(x = 6,y = 9)$ into $y=\frac{a}{x - 4}+k$. When $x = 6$ and $y = 9$, we get $9=\frac{a}{6 - 4}+k=\frac{a}{2}+k$. Let's assume $k = 0$ (a simple case), then $\frac{a}{2}=9$, so $a = 18$.

Answer:

$y=\frac{18}{x - 4}$