A taxi company charges $4.00 for the first mile (or part of a mile) and 40 cents for each succeeding tenth of a mile (or part). Express the cost C (in dollars) of a ride as a piecewise-defined function of the distance x traveled (in miles) for 0 < x ≤ 2.

To express the cost C as a piecewise-defined function, we need to consider the different ranges of distance traveled.

First, let's examine the cost for the first mile (or part of a mile) which is a fixed cost of $4.00 regardless of the distance traveled. We can represent this as:

C(x) = $4.00, for 0 < x ≤ 1

Next, we need to consider the cost for each succeeding tenth of a mile (or part) after the first mile. The cost per tenth of a mile is $0.40. So, for distances greater than 1 mile, we multiply the number of tenths of a mile by $0.40.

For distances greater than 1 mile (1 < x ≤ 2), the number of tenths of a mile is (10x - 10), and we multiply this by $0.40 to get the cost:

C(x) = 0.40(10x - 10), for 1 < x ≤ 2

Therefore, the piecewise-defined function for the cost C as a function of the distance traveled x, for 0 < x ≤ 2 is:

C(x) =
$4.00, for 0 < x ≤ 1
0.40(10x - 10), for 1 < x ≤ 2

try

C(x) = 4.00 + 0.40⌈10x⌉

where ⌈z⌉ is the ceiling function (the least integer greater than z)

For example, ⌈2.37⌉ = 3