Question

in a board game, a certain number of points is awarded to a player upon rolling a six sided die (labeled 1 to 6) according to the function $f(x) = 4x + 1$, where $x$ is the value rolled on the die. find and interpret the given function values and determine an appropriate domain for the function.

$f(4) = \square$, meaning when a $\square$ is rolled on the die, the player is awarded $\square$ points. this interpretation

$f(4.5) = \square$, meaning when a $\square$ is rolled on the die, the player is awarded $\square$ points. this interpretation

$f(9) = \square$, meaning when a $\square$ is rolled on the die, the player is awarded $\square$ points. this interpretation

based on the observations above, it is clear that an appropriate domain for the function is

Explanation:

Step1: Calculate $f(4)$

Substitute $x=4$ into $f(x)=4x+1$:
$f(4)=4(4)+1=16+1=17$

Step2: Calculate $f(4.5)$

Substitute $x=4.5$ into $f(x)=4x+1$:
$f(4.5)=4(4.5)+1=18+1=19$

Step3: Calculate $f(9)$

Substitute $x=9$ into $f(x)=4x+1$:
$f(9)=4(9)+1=36+1=37$

Step4: Define valid domain

A 6-sided die only rolls integers 1 to 6.

Answer:

$f(4) = 17$, meaning when a 4 is rolled on the die, the player is awarded 17 points. This interpretation is not valid in the context of the problem.
$f(4.5) = 19$, meaning when a 4.5 is rolled on the die, the player is awarded 19 points. This interpretation is not valid in the context of the problem.
$f(9) = 37$, meaning when a 9 is rolled on the die, the player is awarded 37 points. This interpretation is not valid in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is $\{1, 2, 3, 4, 5, 6\}$