Question

Joe took $12 to the arcade. Each game cost $.50 to play. This situation can be modeled with the equation y + -.50 x+ 12. This represents the relationship between money Joe has remaining, y, and the number of games he plays, x. Use the function to determine the x-intercept.

State the Domain and Range for this equation in the context of the problem scenario?

Answer 1

x-intercept: x=24

DOMAIN: (0,24) where x∈Natural Numbers

RANGE: (0,12) where y∈Natural Numbers

Explanation:

Remain money = y

Number of games = x

Given function:

`y=12-0.5x\\`

x-intercept:

x-intecept is the value of x where y becomes zero.

Substitute y=0 in the given equation:

`0=12-0.5x\\0.5x=12\\x=(12)/(0.5)\\x=24`

Domain:

Domain is a set of all possible values of x.

x= No. of games (So x cannot be negative)

y= Remain Amount (So y cannot be negative)

So the minimum value of x is 0 because x cannot be negative.

Maximum value of x is the value for which y doesn't become negative. For any value of x>24, y <0 which is not possible.

So maximum value of x is 24

DOMAIN: (0,24) where x∈Natural Numbers

Range:

Range is a set of all outcomes of y for all possible values of x.

For x=0 , y =12

for x=24 , y = 0

So

RANGE: (0,12) where y∈Natural Numbers