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Function Notation

5.8.4 Function Notation

5.8.4 • Function Notation

Cool Down

For questions 1 - 3, the graph shows the population of beavers in a forest for different numbers of years after 1995. The beaver population is growing exponentially.

A scatter plot showing the number of beavers over 5 years. Red points show increases: (1,100), (2,200), (3,400), (4,800). The y-axis is number of beavers and the x-axis is time in years.
1.

Explain why we can think of the beaver population as a function of time in years.

Compare your answer:

The number of beavers depends on time in years. In any given year, there is a particular number of beavers in the forest.

2.

What is the meaning of the point labeled Q Q in this context?

Compare your answer:

The point Q Q indicates that 3.5 years after 1995, the beaver population was about 550.

3.

Write an equation using function notation to represent this situation.

Compare your answer:

p ( t ) = 50 · 2 t p ( t ) = 50 · 2 t where t t  is years after 1995 and p ( t ) p ( t ) is the beaver population at that time.

4.

Which equation is most appropriate for modeling this data?

xx 1 2 3 4 5
yy 14 26 74 266 1034
This table displays corresponding numerical values for variables x and y across five data points, suggesting a functional relationship between them.

  1. y = 10 + ( 4 x ) 2 y = 10 + ( 4 x ) 2

  2. y = 10 + 4 x y = 10 + 4 x

  3. y = 10 + 4 x 2 y = 10 + 4 x 2

  4. y = 10 + 4 1 x y = 10 + 4 1 x

y = 10 + 4 x y = 10 + 4 x