Page 828 - Algebra 1

Example
4
Identifying an Appropriate Model
Identify the appropriate model for each of the following situations.
a. the height of a ball thrown upward from an initial height of 5 feet
SOLUTION
When a ball is thrown upward, it goes up for a short time and then changes direction and comes down again. Its height has a maximum value. Therefore, a quadratic function models this situation.
b. the cost of a tank of gas when gas costs $3.25 per gallon
SOLUTION
The cost of gas is a constant rate. For every additional gallon, the price of the tank of gas increases by $3.25. Therefore, a linear function models this situation.
c. the number of bacteria cells in a laboratory dish when each cell divides into two cells every day
SOLUTION
Imagine the first day there was only one cell in the dish. The next day, there would be 2 cells, and the following day, 4 cells. The number of cells doubles every day, so it is not a constant rate of change but an increasing rate of change. Therefore, an exponential function models this situation.
Identify the function family represented by each graph.
(Ex 1)
a. b. c.
Use the table of values to identify the function family.
(Ex 2)
d.
e.
Tell whether the function family is linear, quadratic, or exponential.
(Ex 3)
f. The graph is always increasing with a constant rate.
g. The graph changes direction at a maximum of 3.
h. The graph is always increasing and it gets steeper as x increases.
Math Reasoning
Formulate Write a function that could be used to find the cost of gas in Example 4b.
Lesson Practice
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Lesson 119 813