Determine the intervals of continuity for the parking cost function c introduced at the outset of this section (see figure). Consider 0≤t≤60. <FIGURE>

Verified step by step guidance

1. Step 1: Understand the problem context. The parking cost function c(t) is defined over the interval 0 \(\leq\) t \(\leq\) 60, where t represents time in minutes.
2. Step 2: Identify the nature of the function. Typically, parking cost functions are piecewise functions, where the cost changes at certain time intervals.
3. Step 3: Determine the points where the function might be discontinuous. These are usually at the boundaries of the piecewise segments.
4. Step 4: Analyze each segment of the piecewise function to check for continuity. A function is continuous on an interval if it is continuous at every point in that interval.
5. Step 5: Conclude the intervals of continuity by excluding any points of discontinuity identified in the previous steps.

Key Concepts

Continuity of Functions

A function is continuous at a point if the limit of the function as it approaches that point equals the function's value at that point. For a function to be continuous over an interval, it must be continuous at every point within that interval. Understanding continuity is essential for analyzing the behavior of the parking cost function over the specified range.

Intervals of Continuity

Intervals of continuity refer to the ranges of input values for which a function remains continuous. To determine these intervals, one must identify points where the function may be undefined or exhibit discontinuities, such as jumps, holes, or vertical asymptotes. This analysis helps in understanding where the parking cost function behaves predictably.

Piecewise Functions

A piecewise function is defined by different expressions based on the input value. In the context of the parking cost function, it may have different rates or rules for different time intervals. Recognizing how piecewise definitions affect continuity is crucial for accurately determining the intervals of continuity for the function.