Question

tommy bought the game of jacks to improve his fine - motor skills. the game came with one rubber ball and 8 metal jack pieces. the ball weighs 1 ounce and each jack weighs 0.25 ounces. if x jacks are added to his hand that contains the ball, the total weight of the ball and jacks can be represented by f(x)=0.25x + 1. what is the range of the function for this situation? a {0, 1, 2, 3, 4, 5, 6, 7, 8} b {1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3} c {0, 2, 4, 6, 8} d {1, 1.5, 2, 2.5, 3}

Explanation:

Step1: Identify valid domain values

The number of jacks $x$ can be 0,1,2,3,4,5,6,7,8 (since there are 8 total jacks).

Step2: Calculate each $f(x)$ value

For $x=0$: $f(0)=0.25(0)+1=1$
For $x=1$: $f(1)=0.25(1)+1=1.25$
For $x=2$: $f(2)=0.25(2)+1=1.5$
For $x=3$: $f(3)=0.25(3)+1=1.75$
For $x=4$: $f(4)=0.25(4)+1=2$
For $x=5$: $f(5)=0.25(5)+1=2.25$
For $x=6$: $f(6)=0.25(6)+1=2.5$
For $x=7$: $f(7)=0.25(7)+1=2.75$
For $x=8$: $f(8)=0.25(8)+1=3$

Step3: Compile the range values

Collect all calculated $f(x)$ values.

Answer:

B. {1, 1.25, 1.5, 1.75, 2, 2.25, 2.5, 2.75, 3}