Lynn Marecek; MaryAnne Anthony-Smith; Andrea Honeycutt Mathis; Jay Abramson; Sharon North; Amy Baldwin; Alyssa Howell

4.10.1 • Analyzing Graphs and Statements in Function Notation

Warm Up

This graph shows the populations of Baltimore and Cleveland in the $20^{th}$ century. $B (t)$ is the population of Baltimore in year t. $C (t)$ is the population of Cleveland in year $t$ .

Line graph showing population trends from 1900 to 2010 for Baltimore (solid blue line) and Cleveland (dashed red line). Both cities peak in mid-1900s, then decline, with Baltimore maintaining a higher population throughout.

1.

Estimate $B (1930)$ and explain what it means in this situation.

Compare your answer:

$B (1930)$ is about 800,000. It’s the population of Baltimore in 1930.

2.

Which statement is true: $B (2000) \geq C (2000)$ or $B (2000) \leq C (2000)$ ?

Answer: $B (2000) \geq C (2000)$

3.

Explain the reasoning for your response to question 2.

Compare your answer:

Your answer may vary, but here is a sample. On the graph, the point that represents $B (2000)$ is located at a higher location than the point that represents $C (2000)$ for each function.

4.

Which statement is true: $B (1900) = C (1900)$ or $B (1900) > C (1900)$ ?

Answer: $B (1900) > C (1900)$

5.

Explain the reasoning for your response to question 4.

Compare your answer:

Your answer may vary, but here is a sample. The blue function representing Baltimore has a higher y-value in 1900 than the red-dashed function representing Cleveland does.

6.

Were the two cities’ populations ever the same? If so, when?

Compare your answer:

Yes. The populations were the same in roughly 1910 and 1943.

4.10.1 Analyzing Graphs and Statements in Function Notation

Warm Up