Properties of Functions Quick Check

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Question
Willow is rereading her favorite book. She starts the day on page 15. Looking at the clock, she realizes that she can read 2 pages every minute. Choose the sketch of a graph that shows the relationship between the number of minutes Willow has been reading today and the page number she is on.(1 point)
Responses

A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.

A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of the plotted closed circle are left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of the plotted closed circle are left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.

A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.
Image with alt text: A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 2 comma 0 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 8 comma 90 right parenthesis.

A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 0 comma 2 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 6 comma 92 right parenthesis
Image with alt text: A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of a plotted closed circle are left parenthesis 0 comma 2 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 6 comma 92 right parenthesis
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1 answer

To sketch the relationship between the number of minutes Willow has been reading and the page number she is on, we need to analyze the information given:

  • Willow starts reading on page 15.
  • She reads 2 pages every minute.

If we let \( x \) represent the number of minutes she has been reading, then after \( x \) minutes, she would be on page: \[ \text{Page number} = 15 + 2x \]

Now we can find a few points:

  • At \( x = 0 \) (the start), she is on page 15: \[ \text{Page number} = 15 + 2(0) = 15 \]

  • After 1 minute ( \( x = 1 \) ): \[ \text{Page number} = 15 + 2(1) = 17 \]

  • After 2 minutes ( \( x = 2 \) ): \[ \text{Page number} = 15 + 2(2) = 19 \]

Continuing this way, we see that the number of pages will keep increasing, forming a straight line with a slope of 2.

Now let's examine the provided options:

  1. The correct starting point for the graph should be at \( (0, 15) \).
  2. The line should be upward slanting, reflecting that she goes up by 2 pages every minute.

Given the criteria above, the correct sketch should be the one that starts at \( (0, 15) \) and has an upward trajectory, correctly calculating pages read over time.

Thus, the correct choice is: A coordinate plane shows the x-axis, labeled as Number of Minutes, ranging from negative 2 to 30 in increments of 2, and the y-axis, labeled as Page Number, ranging from negative 5 to 100 in increments of 5. A ray extends from a plotted point. The coordinates of the plotted closed circle are left parenthesis 0 comma 15 right parenthesis. An upward slanting arrow extends from the plotted point and passes through left parenthesis 30 comma 75 right parenthesis.