Domain of a Linear Function in a Real-World Context
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Jacob is taking part in a month-long reading challenge at his school. He can earn points for each book he reads, up to two dozen books. As shown in the graph, $P(b)$ gives the number of points Jacob earns as a function of the number of books he reads. Complete the sentences. The domain is [dropdown]. The domain represents [dropdown].
This question includes visual content: A Cartesian coordinate system graph titled 'Reading challenge'. The horizontal axis (x-axis) is labeled 'Books read' and ranges from 0 to 30 with increments of 2. The vertical axis (y-axis) is labeled 'Points earned' and represents P(b), ranging from 0 to 150 with increments of 15. A series of discrete points (dots) indicates a linear relationship starting from (0,0) and ending at (24, 120). The points represent the number of points earned per book read.
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Step by Step Written Solution
Jacob is participating in a month-long reading challenge. We're given a graph that shows the relationship between the number of books he reads and the points he earns.
Analyzing the Domain
To complete the sentences, we first need to identify the domain of this function. In a graph, the domain is the set of all possible input values, which are usually plotted along the horizontal x-axis, or in this case, the b-axis for books read.
Domain: Potential input values (horizontal axis)
Let's look at the horizontal axis, labeled labeled 'Books read'. The dots on the graph represent discrete points for every whole book Jacob finishes.
Notice that the graph starts at zero books and continues up to twenty-four books. The problem notes he can earn points for up to two dozen books, and twenty-four is exactly two dozen.
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