Find the constant of variation for each relation and use it to write an equation for each statement. Then solve the equation. If y varies inversely as the square of x and y = 9 when x = 2, find y when x = 3.

Find the constant of variation for each relation and use it to write an equation for each statement. Then solve the equation. If y varies jointly as x and the cube of z and y = 16 when x = 4 and z = 2, find y when x = -8 and z = -3.

Describe how the graphs of f(x) and g(x) are related. $f(x)=x^{3}$ and $g(x)=(x-5)^{3}$

Determine whether each function is continuous at the given x-value. Justify your answer using the continuity test.

$$f(x)=\left\{\begin{array}{l} 3 x+5 \text { if } x \leq-4 \\ -x+2 \text { if } x>-4 \end{array} ; x=-4\right.$$

Determine whether the graph of each function is symmetric with respect to the x-axis, y-axis, the line y = x, the line y = -x, or none of these. $x+y^{2}=4$

Determine the equations of the vertical and horizontal asymptotes, if any, of each function. $g(x)=\frac{x-1}{(2 x+1)(x-5)}$

Graph each function and its inverse. $f(x)=|2 x|$

Determine whether the graph of each function is symmetric with respect to the origin. $f(x)=x^{3}-1$

Determine whether the ordered pair is a solution for the given inequality. Write yes or no. $y>-\sqrt{x+11}+1,(-2,-1)$

Describe how the graphs of f(x) and g(x) are related. $f(x)=|x|$ and $g(x)=|5 x|$

Determine the equations of the vertical and horizontal asymptotes, if any, of each function. $f(x)=\frac{x^{2}}{x+6}$

Determine whether each function is continuous at the given x-value. Justify your answer using the continuity test. $y=\left[ \frac{1}{2} x\right]; x=3$

Find the constant of variation for each relation and use it to write an equation for each statement. Then solve the equation. Suppose y varies jointly as x and z and y = 36 when x = 1.2 and z = 2. Find y when x = 0.4 and z = 3.

Determine whether the graph of each function is symmetric with respect to the x-axis, y-axis, the line y = x, the line y = -x, or none of these. $x y=4$