5) Inswer the questions below for the function: \( f(x)=x^{2}-2 x-3 \) a. Does the parabola open upward or downward? b. Is there a maximum or minimum? c. Find the axis of symmetry. d. Find the vertex. e. Determine the \( y \)-intercept. f. Determine the \( x \)-intercept(s), if they exist. g. Graph the parabola.

lify \( \left(\frac{x^{-2} y^{-1 / 3}}{x^{-5 / 3} y^{-2 / 3}}\right)^{3} \) so there

\[ \begin{array}{l}|x+6| \leq 7\end{array} \] Solve the absolute value inequality. A. The solution set in interval notation is (Simplify your answer.) The solution set is \( \varnothing \).

Given \( f(x)=-3 x+4 \) and \( g(x)=x+7 \), what is the value of \( g(f(2)) ? \)

Determine whether the following equation defines \( y \) as a function of \( x \). \[ x^{2}+y=49 \] Does the equation \( x^{2}+y=49 \) define \( y \) as a function of \( x \) ? Yes No

\[ 11^{-x-4}=4^{3 x} \] Write the exact answer using either base-10 or base-e logarithms. \( x=\square \)