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A museum charges $5 per person for a guided tour with a group of 1 to 9 people or a fixed $50 fee for a group of 10 or more people. Write a function relating the number of people, to the cost,
Two different formulas will be needed. For n -values under 10, For values of that are 10 or greater,
A cell phone company uses the function below to determine the cost, in dollars for gigabytes of data transfer.
Find the cost of using 1.5 gigabytes of data and the cost of using 4 gigabytes of data.
To find the cost of using 1.5 gigabytes of data, we first look to see which part of the domain our input falls in. Because 1.5 is less than 2, we use the first formula.
To find the cost of using 4 gigabytes of data, we see that our input of 4 is greater than 2, so we use the second formula.
Given a piecewise function, sketch a graph.
Sketch a graph of the function.
Each of the component functions is from our library of toolkit functions, so we know their shapes. We can imagine graphing each function and then limiting the graph to the indicated domain. At the endpoints of the domain, we draw open circles to indicate where the endpoint is not included because of a less-than or greater-than inequality; we draw a closed circle where the endpoint is included because of a less-than-or-equal-to or greater-than-or-equal-to inequality.
[link] shows the three components of the piecewise function graphed on separate coordinate systems.
Now that we have sketched each piece individually, we combine them in the same coordinate plane. See [link] .
Can more than one formula from a piecewise function be applied to a value in the domain?
No. Each value corresponds to one equation in a piecewise formula.
Access these online resources for additional instruction and practice with domain and range.
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