A taxi company charges $4.00 for the first mile (or part of a mile) and 80 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.

Answer:The piecewise function is:[tex]C(x) = C(x) = \left \{ {{4, 0< x \leq 1} \atop {4 + 8x, 1 < x \leq 2}}\right. [/tex]Step-by-step explanation:A piecewise function is a function that is defined in multiple intervals.In the first interval:[tex]0 < x \leq 1[/tex]The problem states that a taxi company charges $4.00 for the first mile (or part of a mile).x is the number of miles. SoIf [tex]x \leq 1, C(x) = $4.00[/tex].Second interval:[tex]1 < x \ leq 2[/tex]Here, the cost is defined by a linear function in the following format:[tex]C(x) = C_{0} + rx[/tex]In which [tex]C_{0}[/tex] is the initial price and r is the price paid per mile.The problem states that each succeeding tenth of a mile costs 80 cents. Sowe have the following rule of three.1 mile - r dollars0.1miles - 0.8 dollars[tex]0.1r = 0.8[/tex][tex]r = \frac{0.8}{0.1}[/tex][tex]r = 8[/tex]So, we have[tex]C(x) = 4 + 8x, 1 < x \leq 2[/tex]Piecewise function:The piecewise function is:[tex]C(x) = C(x) = \left \{ {{4, 0< x \leq 1} \atop {4 + 8x, 1 < x \leq 2}}\right. [/tex]