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A self-serve frozen yogurt store sells servings up to 12 ounces. It charges \$0.50 per ounce for a serving between 0 and 8 ounces and \$4 for any serving greater than 8 ounces and up to 12 ounces.
Choose the graph that represents the price as a function of the weight of a serving of yogurt. Be prepared to explain how you know.
A
B
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D
The relationship between the postage rate and the weight of a letter can be defined by a piecewise function.
The graph shows the 2018 postage rates for using regular service to mail a letter.
Horizontal axis, weight in ounces. Scale 0 to 4, by 0 point 5's. Vertical axis, postage in dollars. Scale, 0 to 1 point 5, by 0 pint 2,5's. Piecewise function. open circle at 0 comma 0 point 5 that extends horizontally to 1 comma 0 point 5, where there is a closed circle. open circle at 1 comma 0 point 7,1 that extends horizontally to 2 comma 0 point 7,1, where there is a closed circle. open circle at 2 comma 0 point 9,2 that extends horizontally to 3 comma 0 point 9,2, where there is a closed circle. open circle at 3 comma 1 point 1,3 that extends horizontally to 3 point 5 comma 1 point 1,3, where there is a closed circle.
What is the price of a letter that has the following weight?
Kiran and Mai wrote some rules to represent the postage function, but each of them made some errors with the domain.
Function represents the dollar cost of renting a bike from a bike-sharing service for minutes. Here are the rules describing the function:
Complete the table with the costs for the given lengths of rental.
| (minutes) | (dollars) |
|---|---|
| 10 | |
| 25 | |
| 60 | |
| 75 | |
| 130 | |
| 180 |
Sketch a graph of the function for all values of that are more than 0 minutes and at most 240 minutes.
A piecewise function has different descriptions, or rules, for different parts of its domain.
Function gives the train fare, in dollars, for a child who is years old based on these rules:
The different prices for different ages tell us that function is a piecewise function.
The graph of a piecewise function is often composed of pieces or segments. The pieces could be connected or disconnected. When disconnected, the graph appears to have breaks or steps.
Here is a graph that represents .
A graph, with origin O. The horizontal axis, age, years, scale from 0 to 16 by 1s. The vertical axis, train fare, dollars, scale from 9 to 8 by 1s. A horizontal line segment, with open circle endpoints, begins at 0 comma 0 and ends at 5 comma 0. A horizontal line segment begins with a closed circle at 5 comma 5 and ends with an open circle at 11 comma 5. A line segment begins with a closed circle at 11 comma 7 and ends with an open circle at 16 comma 7.
It is important to consider the value of the function at the points where the rule changes, or where the graph “breaks.” For instance, when a child is exactly 5 years old, is the ride free, or does it cost \$5?
On the graph, one segment ends at and another segment starts at , but the function cannot have both 0 and 5 as outputs when the input is 5!
Based on the fare rules, the ride is free only if the child is under 5, which means:
The same reasoning applies when deciding how and should be shown on the graph.
The fare rules can be expressed with function notation:
A piecewise function is a function defined using different expressions for different intervals in its domain.