A parking lot charges 3 dollars for the first hour (or part of an hour) and 2 dollars for each succeeding hour (or part), up to a daily maximum of 10 dollars. Is this function continuous? (If there are discontinuities, discuss their significance to someone who parks in the lot)

function is discontinuous

and

after 3 hours upto day 24 hours fix charge $10

so there are discontinuous at 1st hour, 2nd hours and 3rd hours

Explanation:

given data

charge = $3 for 1st hour

charge = $2 for each succeeding hour

maximum charge = $10 daily

to find out

Is this function continuous

solution

their function is 3 + 2x

so function is discontinuous here

and

this is very clear for 1st hour or part of hour it mean charge a fix value in given time

anyone who park fix charge for 60 min up to the 3 hours

after that for day 24 hours fix charge $10

so there are discontinuous at 1st hour, 2nd hours and 3rd hours