Activity 1.2

Some definitions… Independent variable is another name for the input variable of a function Independent variable is another name for the input variable of a function Dependent variable is another name for the output variable of a function Dependent variable is another name for the output variable of a function The collection of all replacement values for the input variable is called the domain of that function. The collection of all replacement values for the input variable is called the domain of that function. The practical domain is the input values that make practical sense for a problem. The practical domain is the input values that make practical sense for a problem. The collection of all the output values are called the range of the function. The collection of all the output values are called the range of the function. The practical range are the output values that make sense for the problem. The practical range are the output values that make sense for the problem.

Now it’s time to pump you up (with gas) For today, you are going to pretend that you have a car that has a 20 gallon gas tank. For today, you are going to pretend that you have a car that has a 20 gallon gas tank. There are the two input variables that determine the cost (output) of a fill-up. What are they? There are the two input variables that determine the cost (output) of a fill-up. What are they?

Still trying to pump you up So, we are going to assume that the price of gas is $1.36(9/10). Now the cost of fill-up is only dependent on one variable, the number of gallons pumped. Let’s complete the table: So, we are going to assume that the price of gas is $1.36(9/10). Now the cost of fill-up is only dependent on one variable, the number of gallons pumped. Let’s complete the table: Number of Gallons Cost of fill-up Is the cost of fill-up a function of the number of gallons pumped?

Pump you up (Cont.) Write a verbal statement that describes how the cost of a fill-up is determined. Write a verbal statement that describes how the cost of a fill-up is determined. Let g be the number of gallons of gasoline pumped and c represent the cost of the fill-up. Translate the verbal statement into a symbolic statement (equation) expressing c in terms of g. Let g be the number of gallons of gasoline pumped and c represent the cost of the fill-up. Translate the verbal statement into a symbolic statement (equation) expressing c in terms of g. How could you write this using function notation? How could you write this using function notation?

Using Our Equation… Our function: f(g) = 1.369g Our function: f(g) = 1.369g What do I need to do to evaluate f(5)? What do I need to do to evaluate f(5)? What about f(8)? What about f(8)?

Domain and Range Number of Gallons Cost of fill-up Write the values in this table into ordered pairs. What would the domain be of these ordered pairs? What about the range?

Practical domain and range What do you think the practical domain is for our example? What do you think the practical domain is for our example? What about the practical range? How can we find it? What about the practical range? How can we find it? What would the domain and range be for our function c = 1.369g if it had no connection to this problem? What would the domain and range be for our function c = 1.369g if it had no connection to this problem?