Lesson 5More Graphs of Functions

Learning Goal

Let’s interpret graphs of functions.

Learning Targets

  • I can explain the story told by the graph of a function.

Lesson Terms

  • independent variable
  • radius

Warm Up: Which One Doesn’t Belong: Graphs

Problem 1

Which graph doesn’t belong?

  1. A graph the looks like a U with the vertex touching the x axis.
  2. A graph the looks like a sideways U with the vertex touching the y axis.
  3. A graph starting at the y axis with a horizontal segment, than a a segment going up and to the right and then a horizontal segment
  4. A graph with points plotted but not connected that start on the upper right and goes down, then up, then down to the x axis.

Activity 1: Time and Temperature

Problem 1

The graph shows the temperature between noon and midnight in one day in a certain city.

A graph of time (hours after noon) on the x from 0 to 11, and temperature (degrees F) on the y from 50 to 59. A line starts on the lower left, goes up and curves back down.

  1. Was it warmer at 3:00 p.m. or 9:00 p.m.?

  2. Approximately when was the temperature highest?

  3. Find another time that the temperature was the same as it was at 4:00 p.m.

  4. Did 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.?

  5. Does this graph show that temperature is a function of time, or time is a function of temperature?

  6. When the input for the function is 8, what is the output? What does that tell you about the time and temperature?

Activity 2: Garbage

Problem 1

A photo of a garbage heap.

The graph shows the amount of garbage produced in the US each year between 1991 and 2013.

A scatter plot of years (1990-2015) vs garbage (thousands of tones) (190,000-270,000). Data mainly goes up and to the right with small dips.

  1. Did the amount of garbage increase or decrease between 1999 and 2000?

  2. Did the amount of garbage increase or decrease between 2005 and 2009?

  3. 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.

Problem 2

The graph shows the percentage of garbage that was recycled between 1991 and 2013.

A scatter plot of years from 1990 to 2015 vs percentage recycled from 15% to 27%. The data rises sharply at the start of the graph and then increases gradually and dips at the end.

  1. When was it increasing?

  2. When was it decreasing?

  3. Tell the story of the change in the percentage of garbage recycled in the US over this time period.

Are you ready for more?

Problem 1

Refer to the graph in the first part of the activity.

  1. Find a year where the amount of garbage produced increased from the previous year, but not by as much it increased the following year.

  2. Find a year where the amount of garbage produced increased from the previous year, and then increased by a smaller amount the following year.

  3. Find a year where the amount of garbage produced decreased from the previous year, but not by as much it decreased the following year.

  4. Find a year where the amount of garbage produced decreased from the previous year, and then decreased by a smaller amount the following year.

Lesson Summary

Here is a graph showing the temperature in a town as a function of time after 8:00 p.m.

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 at 8 hours after 8:00 p.m., or 4:00 a.m. Then it starts to increase again.

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.