Evaluating functions is the process of finding the output value of a function for a given input value. To do this, substitute the input value for the variable and then simplify the expression.
Maritza earns $18 an hour tutoring at the community center. On weekends, she is paid a bonus $15 per shift. How much money would Maritza earn for working 6 hours on a Saturday? If x is the number of hours worked, solve the function f(x) for x = 6 hours.
Express using function notation:
Substitute for the input variable:
She would earn $123 working 6 hours on Saturday
The domain and range describe the limits of the function. The domain is the set of all the possible input values. The range is the set of all the possible output values. You need to know the domain BEFORE you can determine the range.
Armando works as a street sign advertiser for a local restaurant. He is paid $10 a shift plus $0.50 for every customer who comes into the restaurant during his shift up to a maximum of $100 per shift. Determine the domain and range of the function that describes Armando’s daily wages.
Express using function notation:
Determine the lower and upper bounds of the domain:
If no constraints are given by the problem, the solution is the set of all real numbers, ℝ
Lower: The fewest customers that can visit is 0
Upper: There is nothing limiting the number of customers that can visit the restaurant, so there is no upper bound
Determine the lower and upper bounds of the range:
Often this comes from the lowest and highest values from the input, but not always!
Lower: The lowest amount Armando can make is $10 if 0 customers visit the restaurant
Upper: If enough customers came, then Armando would hit his maximum salary of $100
Express the domain and range as inequalities:
If only one side is bounded you can use a simple inequality