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. $x^{2}=\frac{1}{y}$

Describe how the graphs of f(x) and g(x) are related. $f(x)=[x]+1$ and $g(x)=-[x]-1$

Determine whether the ordered pair is a solution for the given inequality. Write yes or no. $y \geq 2|x|^{3}-7,(0,0)$

Determine the equations of the vertical and horizontal asymptotes, if any, of each function. $g(x)=\frac{x-2}{x^{2}+4 x+3}$

Determine whether the ordered pair is a solution for the given inequality. Write yes or no. $y \leq \frac{x^{2}-6}{x},(-6,-9)$

Determine whether the graph of each function is symmetric with respect to the origin. $f(x)=\frac{1}{4 x^{7}}$

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. $x=-2 y$

Graph each function and its inverse. $f(x)=x^{3}-2$

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

$$f(x)=\left\{\begin{array}{l} 2 x+1 \text { if } x \geq 1 \\ 4-x^{2} \text { if } x<1 \end{array} ; x=1\right.$$

Describe how the graphs of f(x) and g(x) are related. $f(x)=\frac{1}{x}$ and $g(x)=\frac{3}{x}$

Find the constant of variation for each relation and use it to write an equation for each statement. Then solve the equation. If r varies directly as the square of t and r = 4 when $t=\frac{1}{2},$ find r when $t=\frac{1}{4}$

Determine whether the ordered pair is a solution for the given inequality. Write yes or no. $y<-0.2 x^{2}+9 x-7,(10,63)$

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.

Determine whether the graph of each function is symmetric with respect to the origin. $f(x)=5 x^{2}+6 x+9$