Lesson 6 Well Versed Solidify Understanding

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Write the piecewise function rule for each graph.

Graph each of the piecewise functions.

$g (x) = {\begin{cases} - 2 (x + 4) + 6, & - 4 \leq x \leq 2 \\ 3 (x - 2) - 6, & 2 < x \leq 5 \end{cases}$

$h (x) = {\begin{cases} x + 10, & - 7 \leq x \leq - 3 \\ - 4, & - 2 \leq x \leq 2 \\ - \frac{1}{4} x + 6, & 4 \leq x \leq 8 \end{cases}$

Describe the transformations that will need to occur to the graph of the parent function so the result is the function described.

$r (x) = {(x + 3)}^{2} - 7$

$f (x) = | x - 8 | + 14$

$g (x) = 2 | x + 5 | - 20$

$h (x) = - 3 {(x - 12)}^{2} + 32$

Find the equation of the inverse function for each of the given functions.

$r (x) = 3 x + 7$

$p (x) = x^{2} - 5$ , Domain $x > 0$

$f (x) = \frac{x + 9}{2}$

$h (x) = x^{2} + 6$ , Domain $x > 0$

$k (x) = - 2 x + 4$

$g (x) = \frac{1}{2} x + 9$

$C = 2 π r$ ; solve for $r$ .

$A = \frac{b_{1} + b_{2}}{2} h$ ; solve for $h$ .

$V = π r^{2} h$ ; solve for $h$ .

$V = π r^{2} h$ ; solve for $r$ .