Unit 5, Lesson 5
More Graphs of Functions
Grade 8
5.1
Warm-up
Which three go together? Why do they go together?
5.2
Activity
The graph shows the temperature between noon and midnight in one day in City A.
Graph in a coordinate plane, horizontal, time in hours after noon, 0 to 12 by ones, vertical, temperature in degrees Farenheit, 50 to 60 by ones. The graph starts at 0 comma 50 and climbs slowly, the more quickly as it moves right, going through 2 comma 52 and 4 comma 57 before peaking at 5 point 8 comma 59. The graph then steadily declines as it moves right until it reaches the point 12 comma 52 point 5.
- Is it warmer at 3:00 p.m. or 9:00 p.m.?
- Approximately when is the temperature highest?
- Find another time that the temperature is the same as it is at 4:00 p.m.
- Does the temperature change more between 1:00 p.m. and 3:00 p.m. or between 3:00 p.m. and 5:00 p.m.?
- Does this graph show that temperature is a function of time, or time is a function of temperature?
- When the input for the function is 8, what is the output? What does that tell you about the time and temperature?
5.3
Activity
- The graph shows the amount of garbage produced in the United States each year between 1991 and 2013.
Scatterplot, horizontal, year, 1990 to 2015 by fives, vertical, garbage in thousands of tons, 190,000 to 270,000 by 20,000. Points start at 1991 comma 208,000, and increase steadily to 2007 comma 255,000 except for slight decreases at 1995 and 2001. Between 2006 and 2009, the points decrease, but increase again from 2009 to 2014.
- Did the amount of garbage increase or decrease between 1999 and 2000?
- Did the amount of garbage increase or decrease between 2005 and 2009?
- Between 1991 and 1995, the garbage increased for three years, and then it decreased in the fourth year. Describe how the amount of garbage changed in the years between 1995 and 2000.
- The graph shows the percentage of garbage that was recycled between 1991 and 2013.
A scatterplot, horizontal, year, 1900 to 2015 by fives, vertival, percentage recycled, 15 % to 27 % by threes. Beginning with 1991 comma 16%, points trend linearly upward to 1996 comma 22%, then linearly upward at a less steep rate to 2011 comma 26 %, then two points trend down.
- When is the graph increasing?
- When is the graph decreasing?
- Tell the story of the change in the percentage of garbage recycled in the United States over the time period shown in the graph.
Student Lesson Summary
Here is a graph showing the temperature in a town as a function of hours after 8:00 p.m.
The graph of a curve on the coordinate plane. The horizontal axis is labeled “time in hours after 8 pm” and the numbers 1 through 11 are indicated. The vertical axis is labeled “temperature in degrees Fahrenheit” and the numbers 45 through 60, in increments of 3 are indicated. The curve starts on the vertical axis at the point 0 comma 60, and moves downwards and to the right. It continues downward until reaching a minimum point of 8 comma 45, turns, and then moves upward and to the right, passing through the point 11 comma 57.
The graph of a function tells us what is happening in the context the function represents. In this example, the temperature starts out at F at 8:00 p.m. It decreases during the night, reaching its lowest point about 8 hours after 8:00 p.m., or 4:00 a.m. Then it starts to increase again.
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