Sketch a graph of $f\left(x\right)=2x+3$.

Write down the coordinates of the vertex of the graph of $y=x^2+6x+8$.

Use your graphing software to draw the following pair of curves on the given axes. In the following case, describe briefly in words how the first curve must be transformed to match the second curve.

$y=x^4-2x^3$ and $y=x^4+2x^3-2x-1$

Use $x$-values of $-3$ to $3$ and $y$-values of $-3$ to $5$.

Use your graphing software to draw the following pair of curves on the given axes. In the following case, describe briefly in words how the first curve must be transformed to match the second curve.

$y=0.5\left(x+5\right)\sqrt{4-x}$ and $y=\frac{1}{2}\sqrt{x+4}\left(5-x\right)$

Use $x$-values of $-10$ to $10$ and $y$-values of $-6$ to $6$.

Without using graphing software or a calculator or finding any specific coordinates of points, sketch the graph of the following function. Label any intercepts with the axes

$y=(x+2{)}^2$

Draw a coordinate plane with axes from $-10$ to $10$.

Plot, these points: $(-4,-5), (-3, -2), (-2, 0), (-1, 1), (0, 0), (1, -1), (4, 1) \text{and} (5, 3)$.

This set of eight points defines the function $f\left(x\right)$. Join the points with a smooth curve.

A change is applied to $f\left(x\right)$ to give a new function $g_1\left(x\right)$. This change is defined as $g_1\left(x\right)=2f\left(x\right)$.

Write down the coordinates of the eight points of $g_1\left(x\right)$.