Sketch the graph of the following piecewise function.

$u\left(x\right)=\{\begin{array}{c}2x-5\frac{}{},\text{ if }x\le 0\\ -x-5,\text{ if }x>0\end{array}$

Consider the following equation,

$y=x^7-7x^5-9$

Find if the graph would be symmetric about the x-axis, the y-axis, the origin, or none of them.

Determine the type of symmetry for the graph represented by the equation $4y^2-x^2=16$.

Solve for the exact value of the following trigonometric expression.

$\sec \left(\frac{23\pi }{2}\right)$

Sketch the graph of the following smallest integer function.

$f\left(x\right)=\lceil x\rceil ,-2\le x\le 2$

The ellipse shown below is defined by the equation $4x^2+y^2=4$. It consists of four one-to-one functions: $g_1\left(x\right)$, $g_2\left(x\right)$, $g_3\left(x\right)$, and $g_4\left(x\right)$. What is the formula and domain for the function $g_3\left(x\right)$?

Given the function $y=g\left(x\right)$, how would the graph of $y=-5g\left(x\right)$ differ from the original graph?

Apply the transformations on the graph of $p\left(x\right)=\sqrt{x}$ into the graph of $h\left(x\right)=4p(3x-2)$. Check your work with the help of a graphing calculator.