Remember we can use any variable to name the function; the notation us that depends h(a) h on The value must be put into the function to get a result. Be careful - the a. “a” “h” parentheses indicate that age is input into the function (Note: do not confuse these parentheses with multiplication!). Function Notation The notation output = defines a function named f(input) f. This would be read is of input” f “output Example 2 A function gives the number of police officers, in a town in year What does N = f(y) N, y. = 300 tell us? f(2005) When we read = 300, we see the quantity is 2005, which is a value for the input f(2005) quantity of the function, the year (y). The output value is 300, the number of police officers (N), a value for the output quantity. Remember So this tells us that in the year 2005 N=f(y). there were 300 police officers in the town. Tables as Functions Functions can be represented in many ways: Words (as we did in the last few examples), tables of values, graphs, or formulas. Represented as a table, we are presented with a list of input and output values. This table represents the age of children in years and their corresponding heights. While some tables show all the information we know about a function, this particular table represents just some of the data available for height and ages of children. age in years 5 5 6 7 8 9 10 a, (output) height inches 40 42 44 47 50 52 54 h, Example 3 Which of these tables define a function (if any)? The and second tables define functions. In both, each input corresponds to exactly one output. The third table does not define a function since the input value of 5 corresponds with two different output values. Solving and Evaluating Functions: When we work with functions, are two typical things we do: evaluate and solve. Evaluating a function is what we do when we know an input, and use the function to determine the
Remember we can use any variable to name the function; the notation h(a) us that h depends on a. The value “a” must be put into the function “h” to get a result. Be careful - the parentheses indicate that age is input into the function (Note: do not confuse these parentheses with multiplication!). Function Notation The notation output = f(input) defines a function named f. This would be read “output is f of input” Example 2 A function N = f(y) gives the number of police officers, N, in a town in year y. What does f(2005) = 300 tell us? When we read f(2005) = 300, we see the quantity is 2005, which is a value for the input quantity of the function, the year (y). The output value is 300, the number of police officers (N), a value for the output quantity. Remember N=f(y). So this tells us that in the year 2005 there were 300 police officers in the town. Tables as Functions Functions can be represented in many ways: Words (as we did in the last few examples), tables of values, graphs, or formulas. Represented as a table, we are presented with a list of input and output values. This table represents the age of children in years and their corresponding heights. While some tables show all the information we know about a function, this particular table represents just some of the data available for height and ages of children. a, age in years 5 5 6 7 8 9 10 (output) h, height inches 40 42 44 47 50 52 54 Example 3 Which of these tables define a function (if any)? The and second tables define functions. In both, each input corresponds to exactly one output. The third table does not define a function since the input value of 5 corresponds with two different output values. Solving and Evaluating Functions: When we work with functions, are two typical things we do: evaluate and solve. Evaluating a function is what we do when we know an input, and use the function to determine the
BusCalc_Chp1_wExercises.docx