Question

on the right are four functions, each using one of the function representations weve learned about in this lesson. use functions: $f(x)$, $g(x)$, $h(x)$ and $k(x)$ to answer the questions on the left.1. $f(-1) = \underline{\quad\quad}$evaluate $f(-1)$determine $x$ when $f(x) = -1LXB0x = \underline{\quad\quad}$3. $h(3) = \underline{\quad\quad}$evaluate $h(3)$determine $x$ when $h(x) = 201LXB1x = \underline{\quad\quad}$(with corresponding function representations: the graph of $f(x)$, the set of ordered pairs for $g(x)$: ${(0,126),(24,96),(48,66),(72,36),(96,6),(120,-24),(144,-54),(168,-84),(192,-114)}$, the table for $h(x)$, and the formula $k(x)=-3x + 89$)

Explanation:

Step1: Find $f(-1)$ from graph

Locate $x=-1$ on $f(x)$ graph, $y=2$.

Step2: Find $x$ when $f(x)=-1$

Locate $y=-1$ on $f(x)$ graph, $x=2$.

Step3: Calculate $g(72)$ via formula

$g(x)=-3x+13$, substitute $x=72$:

$$\begin{align*} g(72)&=-3(72)+13\\ &=-216+13\\ &=-203 \end{align*}$$

Step4: Solve $g(x)=22$ for $x$

Set $-3x+13=22$:

$$\begin{align*} -3x&=22-13\\ -3x&=9\\ x&=-3 \end{align*}$$

Step5: Find $h(3)$ from table

Locate $x=3$ in $h(x)$ table, $h(3)=70$.

Step6: Find $x$ when $h(x)=203$

Locate $y=203$ in $h(x)$ table, $x=8$.

Step7: Calculate $p(11)$ from set

Locate $x=11$ in $p(x)$ set, $p(11)=45$.

Step8: Solve $p(x)=56$ for $x$

Locate $y=56$ in $p(x)$ set, $x=7$.

Answer:

$f(-1)=2$
$x=2$ when $f(x)=-1$
$g(72)=-203$
$x=-3$ when $g(x)=22$
$h(3)=70$
$x=8$ when $h(x)=203$
$p(11)=45$
$x=7$ when $p(x)=56$