Question

practice part 3
not all functions are equations- some are represented graphically, with tables, etc. we can still use function notation to represent the inputs and outputs.

a. $f(4) = \underline{\quad\quad}$
b. $f(2) = \underline{\quad\quad}$
c. when $f(x)=1, x=\underline{\quad\quad}$
d. $f(x)=4$, what is x?$\underline{\quad\quad}$

x	1	2	3	4	5

a. $h(4) = \underline{\quad\quad}$ b. $h(x)=60, x=\underline{\quad\quad}$

a. $g(1) = \underline{\quad\quad}$
b. $g(6) = \underline{\quad\quad}$
c. when $g(x)=1, x=\underline{\quad\quad}$
d. $g(x)=6$, what is x?$\underline{\quad\quad}$

x	0	2	4	6	8

a. $q(8) = \underline{\quad\quad}$ b. $q(x)=1, x=\underline{\quad\quad}$

practice part 4
interpret the following within the context of the scenario.

the amount of money in jareds bank account is modeled by the function $f(x)=105x + 450$, where x is the time in weeks. interpret $f(7)=1185$.

the height of a rocket (in meters) can be represented by the function $h(x)=-\frac{31}{2}x^2 + 1100x$ where x is the time in seconds since the rocket is launched. interpret $h(70.96774)=0$.

Explanation:

Step1: Find $f(4)$ from graph

Locate $x=4$ on $y=f(x)$, $y=4$.

Step2: Find $f(2)$ from graph

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

Step3: Find $x$ when $f(x)=1$

Locate $y=1$ on $y=f(x)$, $x=3$.

Step4: Find $x$ when $f(x)=4$

Locate $y=4$ on $y=f(x)$, $x=1,5$.

Step5: Find $h(4)$ from table

Locate $x=4$ in $h(x)$ table, $h(4)=40$.

Step6: Find $x$ when $h(x)=60$

Identify pattern $h(x)=10x$, solve $10x=60$ → $x=6$.

Step7: Find $g(1)$ from graph

Locate $x=1$ on $y=g(x)$, $y=2$.

Step8: Find $g(6)$ from graph

Locate $x=6$ on $y=g(x)$, $y=7$.

Step9: Find $x$ when $g(x)=1$

Locate $y=1$ on $y=g(x)$, $x=0$.

Step10: Find $x$ when $g(x)=6$

Locate $y=6$ on $y=g(x)$, $x=5$.

Step11: Find $q(8)$ from table

Locate $x=8$ in $q(x)$ table, $q(8)=256$.

Step12: Find $x$ when $q(x)=1$

Locate $q(x)=1$ in table, $x=0$.

Step13: Interpret $f(7)=1185$

$x$ = weeks, $f(x)$ = bank balance: After 7 weeks, Jared has $1185 in his account.

Step14: Interpret $h(70.96774)=0$

$x$ = seconds, $h(x)$ = rocket height: After 70.96774 seconds, the rocket has returned to ground level (height = 0 meters).

Answer:

Practice Part 3

For $y=f(x)$:

a. $4$
b. $2$
c. $3$
d. $1, 5$

For $h(x)$ table:

a. $40$
b. $6$

For $y=g(x)$:

a. $2$
b. $7$
c. $0$
d. $5$

For $q(x)$ table:

a. $256$
b. $0$

Practice Part 4

1. After 7 weeks, the amount of money in Jared's bank account is $1185.
2. 70.96774 seconds after the rocket is launched, the rocket has a height of 0 meters (it has landed back on the ground).