Sketch a graph of \( f \) \( f(x)=2 x-x^{2} \)

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) d) Determine the symmetry of the graph. Odd; origin symmetry Even; \( y \)-axis symmetry Neither

Use transformations of the absolute value function, \( \mathrm{f}(\mathrm{x})=|\mathrm{x}| \), to graph the function \( g(x)=-|\mathrm{x}-3|-5 \). ... \( \square \) A. Horizontal shift \( \square \) B. Vertical stretch/shrink \( \square \) C. Horizontal stretch/shrink \( \square \) D. Vertical shift \( \square \) E. Reflection about the \( x \)-axis \( \square \) F. Reflection about the \( y \)-axis

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)

Suppose that the functions \( f \) and \( g \) are defined as follows. \[ \begin{array}{l}f(x)=\sqrt{5 x+3} \\ g(x)=3 x^{2}+1\end{array} \] Find \( f+g \) and \( f \cdot g \). Then, give their domains using interval notation.

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-2} \) To graph the function, first determine the symmetry of the graph of f . Choose the correct answer below. y-axis symmetry origin symmetry neither \( y \)-axis symmetry nor origin symmetry What is the \( y \)-intercept? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The \( y \)-intercept is (Type an integer or a simplified fraction.)