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Algebra 1

4.10.2 Interpreting Graphs and Statements in Terms of a Situation

Algebra 14.10.2 Interpreting Graphs and Statements in Terms of a Situation
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Activity

H(t)H(t) is the percentage of homes in the United States that have a landline phone in year tt. C(t)C(t) is the percentage of homes with only a cell phone. Here are the graphs of HH and CC.

Line graph showing percentage of homes with landline phones decreasing from 2004 to 2016, while cell phone only homes increase over the same period. Landlines drop below 50% and cell-only rises above 40% by 2016.

1. Estimate H(2006)H(2006).

2. Explain what this value tells us about the phones.

3. Estimate C(2006)C(2006).

4. Explain what this value tells us about the phones.

5. What is the approximate solution to C(t)=20C(t)=20?

6. Explain what the solution to C(t)=20C(t)=20 means in this situation.

7. Is this equation true: C(2011)=H(2011)C(2011)=H(2011)?

8. Explain how you know if the equation is true or not.

9. Is this equation true: C(2015)=H(2015)C(2015)=H(2015)?

10. Explain how you know if the equation is true or not.

11. Between 2004 and 2015, did the percentage of homes with landlines decrease at the same rate at which the percentage of cell-phones-only homes increased?

12. Explain the reasoning for your response to question 11.

Self Check

A Mars rover collected the following temperature data over 1.6 Martian days. A Martian day is called a Sol. The graph below displays the air and ground temperatures in Celsius ( y -axis) for specific times measured in Sols ( x -axis). Which of the following is true about the comparison between ground temperature and air temperature?

GRAPH THAT SHOWS AIR TEMPERATURE AND GROUND TEMPERATURE IN DEGREES CELSIUS FOR 10 TO 11.6 SOLS.

  1. The air temperature is always warmer than the ground temperature.
  2. At 11 Sols, the air temperature is warmer than the ground temperature.
  3. The ground temperature is always warmer than the air temperature.
  4. At 11 Sols, the ground temperature is warmer than the air temperature.

Additional Resources

Comparing Populations

Graphs are very useful for comparing two or more functions. Here are graphs of functions CC and TT, which give the populations (in millions) of California and Texas in year xx.

Line graph showing the population growth of California and Texas from 1910 to 2010; Californias population rises more steeply, surpassing 35 million, while Texas grows steadily to just over 25 million.
What can we tell about the populations? How can we tell? How can we convey this with function notation?
In the early 1900s, California had a smaller population than Texas. The graph of CC is below the graph of TT when xxis 1900. C(1900)<T(1900)C(1900)<T(1900)
Around 1935, the two states had the same population of about 5 million people. The graphs intersect at about (1935,5)(1935,5). C(1935)=5C(1935)=5 and T(1935)=5T(1935)=5, and C(1935)=T(1935)C(1935)=T(1935)
After 1935, California has had more people than Texas. When xx is greater than 1935, the graph of C(x)C(x) is above that of T(x)T(x). C(x)>T(x)C(x)>T(x) for x>1935x>1935
Both populations have increased over time, with no periods of decline. Both graphs slant upward from left to right.  
From 1900 to 2010, the population of California has risen faster than that of Texas. California had a greater average rate of change. If we draw a line to connect the points for 1900 and 2010 on each graph, the line for C has a greater slope than that for T. C(2010)−C(1900)201−1900>T(2010)−T(1900)2010−1900C(2010)−C(1900)201−1900>T(2010)−T(1900)2010−1900

Try it

Try It: Comparing Populations

Examine the graph given above that displays the populations of California and Texas over time.

1. Which state had a greater population in 1920?

2. Write a true mathematical statement using function notation to describe which state has the greater population in 1920.

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