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1-196.

Given the tables below: .

 $x$ $–2$ $–1$ $0$ $1$ $2$ $3$ $10$ $100$ $f(x)$ $–11$ $–8$ $–5$ $–2$ $1$ $4$ $25$ $295$

 $x$ $−3$ $–2$ $–1$ $0$ $1$ $2$ $3$ $12$ $g(x)$ $–5$ $0$ $3$ $4$ $3$ $0$ $–5$ $−140$

 $x$ $−2π$ $−π$ $0$ $\frac { \pi } { 2 }$ $π$ $\frac { 3 \pi } { 2 }$ $2π$ $12π$ $h(x)$ $2$ $–2$ $2$ $0$ $–2$ $0$ $2$ $2$
1. Write possible equations for the functions $f$, $g$, and $h$.

$f(x)$ looks linear.
$g(x)$ looks quadratic.
$h(x)$ looks trigonometric.
Find a transformation that works for each of them.

2. Evaluate:

These composite functions can be evaluated with the table.You do not need to use the equations from part (a).

1. $f(g(h(π)))$

$h(π) = −(2)$
$g(−2) = 0$
$f(0) = −5$
so $f(g(h(π))) = −5$

2. $h(g^{–1}(4))$

$g^{ −1}(4)$
Translation: On the $g(x)$ table, what $x$-value has a $y$-value of $4$? Use the table... do NOT find the inverse function... that would be a waste of time!

3. $f^{ –1}(h(π))$

Refer to hint in part (ii).

$f ^{−1}(h(π)) = 1$

Use the eTool below to explore.
Click the link at right for the full version of the eTool: Calc 1-196 HW eTool