which statement(s) about the function is corr...
which statement(s) about the function is correct? f(x)=-4/(x² - 6x) 1. there are no horizontal asymptotes. 2. this function has 3 total asymptotes. 3. the equation for a vertical asymptote of this function is x = 6. 4. there is only one vertical asymptote. i only ii and iii only iii only iv only
Answer
# Explanation:
## Step1: Find horizontal asymptotes
Degree of denominator ($n = 2$) is greater than degree of numerator ($m=0$). So, $\lim_{x\rightarrow\pm\infty}\frac{- 4}{x^{2}-6x}=0$. There is a horizontal asymptote $y = 0$. So statement 1 is false.
## Step2: Find vertical asymptotes
Set the denominator equal to zero: $x^{2}-6x=x(x - 6)=0$. Solving $x(x - 6)=0$ gives $x = 0$ and $x=6$. So there are two vertical - asymptotes $x = 0$ and $x = 6$. The function has 2 vertical asymptotes and 1 horizontal asymptote, a total of 3 asymptotes. So statement 2 is true, statement 3 is true, and statement 4 is false.
# Answer:
II and III only