Donald fills his gas tank before leaving in a trip. His car uses gasoline at a constant rate and the amount of gasoline , g , remaining after m miles cab be modeled by m + 20g = 640 . Select the correct values to complete the range of the function in context. ( check image for options )
{ g | ≤ g ≤ }

The equation [tex]$ m + 20g = 640 $[/tex] describes the relationship between the number of miles driven, [tex]$ m $[/tex], and the amount of gasoline remaining, [tex]$ g $[/tex]

To find the range of the function, we need to determine the values of [tex]$ g $[/tex] when the tank is full (before the trip starts, when [tex]$ m = 0 $[/tex]) and when the tank is empty (after Donald has driven as far as possible with the gasoline, when [tex]g = 0[/tex])

When the tank is full (at the start of the trip), [tex]$ m = 0 $[/tex]. Plugging this into the equation gives us the amount of gasoline when the tank is full:

[tex]\[ 0 + 20g = 640 \][/tex]

[tex]\[ g = 32 \][/tex]
When the tank is empty, there is no gasoline left, so [tex]$ g = 0 $[/tex]. At that point, Donald would have driven the maximum number of miles:
[tex]\[ m + 20(0) = 640 \][/tex]

[tex]\[ m = 640 \][/tex]

So, the range of the function is all the values that [tex]$ g $[/tex] can take, from full (32 gallons) to empty (0 gallons). Therefore, the correct range is:

[tex]\[ \{ g | 0 \leq g \leq 32 \} \][/tex]