Park an additional hour and the charge is $16. Park for two hours and five minutes and the charge is $12. Suppose a parking garage charges $4.00 per hour or fraction of an hour, with a $25 per day maximum charge. Let’s create the function D, D, where D ( x ) D ( x ) is the output representing cost in dollars for parking x x number of hours. If temperature represents a continuous function, what kind of function would not be continuous? Consider an example of dollars expressed as a function of hours of parking. Temperature as a function of time is an example of a continuous function. A function that has no holes or breaks in its graph is known as a continuous function. At no point did the temperature cease to exist, nor was there a point at which the temperature jumped instantaneously by several degrees. There are no breaks in the function’s graph for this 24-hour period. This means all real numbers in the output between 96 ∘ F 96 ∘ F and 118 ∘ F 118 ∘ F are generated at some point by the function according to the intermediate value theorem, In fact, any temperature between 96 ∘ F 96 ∘ F and 118 ∘ F 118 ∘ F occurred at some point that day. and 4 p.m., the temperature outside must have been exactly 110.5 ∘ F. the temperature had risen to 116 ∘ F, 116 ∘ F, and by 4 p.m. The graph in Figure 1 indicates that, at 2 a.m., the temperature was 96 ∘ F 96 ∘ F. Let’s consider a specific example of temperature in terms of date and location, such as June 27, 2013, in Phoenix, AZ. Determining Whether a Function Is Continuous at a Number In this section, we will investigate functions with and without breaks. This single observation tells us a great deal about the function. We could trace the graph without picking up our pencil. When we analyze this graph, we notice a specific characteristic. Figure 1 Temperature as a function of time forms a continuous function.
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