Graph the logarithmic function \( g(x)=-3-\log _{4} x \). To do this, plot two points on the graph of the function, and also draw the asymptote. Additionally, give the domain and range of the function using interval notation.

Select the correct answer Which function's domain consists of only real numbers greater than 3 ? A. \( f(x)=3 x \) B. \( f(x)=\sqrt{x} \) C. \( f(x)=3 x+4 \) D. \( f(x)=\frac{1}{\sqrt{x-3}} \)

2. \( y=\left\{\begin{array}{ll}1, & \text { if } 0 \leq x<3 \\ 0, & \text { if } 3 \leq x<6 \\ -1, & \text { if } 6 \leq x<9 \\ -2, & \text { if } 9 \leq x<12\end{array}\right. \)

The domain of \( f(x) \) is the set of all real values except 7 , and the domain of \( g(x) \) is the set of all real values except -3 . Which of the following describes the domain of \( (g \circ f)(x) \) ? all real values except \( x \neq-3 \) and the \( x \) for which \( f(x) \neq 7 \) all real values except \( x \neq-3 \) and the \( x \) for which \( f(x) \neq-3 \) all real values except \( x \neq 7 \) and the \( x \) for which \( f(x) \neq 7 \) all real values except \( x \neq 7 \) and the \( x \) for which \( f(x) \neq-3 \)

Find all vertical asymptotes of the following functio \[ f(x)=\frac{4 x^{2}-1}{6 x^{2}-15 x-9} \]

Let \( x>3 \) and \( y>0 \). Using the laws of logarithms, the expanding form of the expression \( \ln \left(\frac{x^{4} y}{\sqrt{x-3}}\right) \) is: