The document discusses modeling and graphing functions. It provides examples of writing a function to model a real-world situation, finding the value of x given a function f(x), and using a function to predict a value. Specifically, it shows a function f(x) = 37x + 7 that models the gray wolf population in Idaho over time, and asks to find the value of x when f(x) = 155 using that model.

1. Find an x -value EXAMPLE 2 Write original function . Substitute 6 for f ( x ). Solve for x . 8 x = ANSWER When x = 8, f ( x ) = 6. 6 2 x – 10 = f ( x ) = 6. For the function f ( x ) 2 x – 10 , find the value of x so that = = 2 x – 10 f ( x )

2. Graph a function EXAMPLE 3 The gray wolf population in central Idaho was monitored over several years for a project aimed at boosting the number of wolves. The number of wolves can be modeled by the function f ( x ) = 37 x + 7 where x is the number of years since 1995. Graph the function and identify its domain and range. GRAY WOLF

3. EXAMPLE 3 SOLUTION To graph the function, make a table. The domain of the function is x  0 . From the graph or table, you can see that the range of the function is f ( x )  7. Graph a function EXAMPLE 3 37(2) + 7 = 81 2 37(1) + 7 = 44 1 37(0) + 7 = 7 0 f(x) x

4. EXAMPLE 5 GUIDED PRACTICE for Examples 2 and 3 2. WOLF POPULATION Use the model from Example 3 to find the value of x so that f ( x ) = 155 . Explain what the solution means in this situation. 4 ; in 1999, 4 years after 1995 , the wolf population will be 155 . ANSWER