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This graph shows the populations of Baltimore and Cleveland in the 20th century. is the population of Baltimore in year . is the population of Cleveland in year .
Here are pairs of statements about the two populations. In each pair, which statement is true? Be prepared to explain how you know.
is the percentage of homes in the United States that have a landline phone in year . is the percentage of homes with only a cell phone. Here are the graphs of and .
Graph of 2 functions. Blue solid line, H of t, represents percentage of homes in US with a landline phone in year t. Red dotted line, C of t, represents the percentage of homes with only a cell phone. H of 2006 is about 85. C of 2006 is about 14. C of 2008= 20. Lines intersect in 2015. The rate of increase in percentage of cell phones is increasing at approximately the same rate as the rate of home phones is decreasing.
Determine if each equation is true. Be prepared to explain how you know.
The number of people who watched a TV episode is a function of that show’s episode number. Here are three graphs of three functions—, and —representing three different TV shows.
Show A10 data points on coordinate plane, no grid, origin O. Horizontal axis, episode number, from 0 to 10 by 2’s. Vertical axis, audience in millions, from 0 to 2 by 0 point 5s. Approximate data points as follows: 1 comma 0 point 75, 2 comma 0 point 9, 3 comma 0 point 95, 4 comma 1 point 25, 5 comma 1 point 3, 6 comma 1 point 4, 7 comma 1 point 75, 8 comma 1 point 6, 9 comma 1 point 8, 10 comma 2.
Show BA graph, with origin O. The horizontal axis, episode number, scale from 0 to 10 by 2s. The vertical axis, audience in millions, scale from 0 to 6 by 1s. Points plotted are 1 comma 9.8, 2 comma 6.1, 3 comma 4.7, 4 comma 4.5, 5 comma 4.3, 6 comma 4.1, 7 comma 3.6, 8 comma 3.2, 9 comma 3.1, and 10 comma 3.0.
Show C10 data points on coordinate plane, no grid, origin O. Horizontal axis, episode number, from 0 to 10 by 2’s. Vertical axis, audience in millions, from 0 to 6 by 1’s. Approximate data points as follows: 1 comma 2 point 5, 2 comma 2 point 6, 3 comma 2 point 4, 4 comma 2 point 5, 5 comma 5 point 5, 6 comma 4, 7 comma 3, 8 comma 2 point 9, 9 comma 2 point 5, 10 comma 2 point 5.
Match each description with a graph that could represent the situation described. One of the descriptions has no corresponding graph.
Sketch a graph of the viewership of the fourth TV show that did not have a matching graph.
Here are graphs that represent two functions, and .
Decide which function value is greater for each given input. Be prepared to explain your reasoning.
A graph, with origin O. The horizontal axis, scale from 9 to 12 by 1s. The vertical axis, scale from 0 to 9 by 1s. A curve, shaped like a U, opening downward and labeled f passes through the points 4 comma 7 and 9 comma 7. It has a maximum at the point 6 comma 8. A line, labeled g, passes through the points 0 comma 8, 4 comma 7, and 9 comma 7.
Graphs are very useful for comparing two or more functions. Here are graphs of functions and , which give the populations (in millions) of California and Texas in year .
Graph of the populations of two states over time on a coordinate plane. Horizontal axis scale 1900 to 2010 by 10’s, labeled “year”. Vertical axis scale 0 to 40 by 10’s, labeled “population in millions”. California has a solid blue graph and Texas is a red dashed graph. California has the points (0 comma 2), (1940 comma 5), (1970 comma 20) and (2010 comma 37). Texas has the points (0 comma 4), (1940 comma 5), (1960 comma 10), (1970 comma 11) and (2010 comma 25).
| What can we tell about the populations? |
How can we tell? | How can we convey this with function notation? |
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In the early 1900s, California had a smaller population than Texas. |
The graph of is below the graph of when is 1900. |
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Around 1935, the two states had the same population of about 5 million people. |
The graphs intersect at about . |
and , and . |
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After 1935, California has had more people than Texas. |
When is greater than 1935, the graph of is above that of . |
for |
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Both populations have increased over time, with no periods of decline. |
Both graphs slant upward from left to right. |
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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 has a greater slope than that for . |
Begin fraction. Begin numerator. C open parenthesis 2010 close parenthesis minus C open parenthesis 1900 close parenthesis . End numerator. Begin denominator. 2010 minus 1900. End denominator. End fraction. Greater than. Begin fraction. Begin numerator. T open parenthesis 2010 close parenthesis ses minus T open parenthesis 1900 close parenthesis . End numerator. Begin denominator. 2010 minus 1900. End denominator. End fraction.
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