Final answer:
The function for the average price of movie tickets is f(x) = 0.10x + 2.75. The domain is 0 to 20 (Years 1980-2000), and the range is $2.75 to $4.75. The ticket price was $4.55 in the year 1998.
Step-by-step explanation:
The average price of movie tickets in the US from 1980 to 2000 can be represented by the function f(x) = 0.10x + 2.75, where x is the number of years since 1980. To graph this function, plot the y-intercept at f(0) = 2.75, and use the slope of 0.10 to find other points. For each additional year, the price increases by $0.10.
The domain of this function, considering the year range given, would be from x = 0 to x = 20 (years 1980 to 2000). The range would be the set of all possible prices over those years, which can be calculated using the function for the years in the domain, yielding a range from $2.75 to $4.75.
To find the year when the movie ticket price was $4.55, set the function equal to $4.55 and solve for x:
4.55 = 0.10x + 2.75
x = (4.55 - 2.75) / 0.10
x = 18
Thus, the movie ticket price was $4.55 in the year 1998 (1980 + 18).