Question

In a board game, a certain number of points is awarded to a player upon rolling a sixsided die (labeled 1 to 6) according to the function f(x) = 4x +3, where x is thevalue rolled on the die. Find and interpret the given function values and determine anappropriate domain for the function.

Answer 1

11, 2, 11, makes sense

25, 5.5, 25, does not makes sense

31, 7, 31, does not makes sense

Intergers in a <= x <= b

a = 1 and b = 6

Explanation:

We have the following function:

`f(x)=4x+3`

where x is the value rolled on the die

The die can land on the numbers 1, 2, 3, 4, 5 and 6.

Therefore:

when x is 2:

`\begin{gathered} f(2)=4\cdot2+3=8+3=11 \\ f(2)=11 \end{gathered}`

f(2) = 11, meaning when a 2 is rolled on the die, the player is awarded 11 points. This interpretation makes sense in the context problem.

when x is 5.5:

`\begin{gathered} f(5.5)=4\cdot5.5+3=22+3=25 \\ f(5.5)=25 \end{gathered}`

f(5.5) = 25, meaning when a 5.5 is rolled on the die, the player is awarded 25 points. This interpretation does not makes sense in the context problem.

when x is 7:

`\begin{gathered} f(7)=4\cdot7+3=28+3=31 \\ f(7)=31 \end{gathered}`

f(7) = 31, meaning when a 7 is rolled on the die, the player is awarded 31 points. This interpretation does not makes sense in the context problem.

Based on the observations above, it is clear that an appropiate domain for the funcion is intergers in a <= x <= b

a = 1 and b = 6