Lesson Plan - Get It!
Torrence works at a restaurant over the summer. He makes $81 a day plus 67% of whatever tips he earns from customers.
During his shift on Wednesday, he earned $153 in tips. The restaurant was slow on Thursday, and he only earned $79 in tips. However, on Friday, he earned $215 in tips.
Torrence wants to calculate how much money he made over these three shifts. He also wants to set up an equation to easily find out how much money he makes at the end of each shift.
- How can we help Torrence?
In order to help Torrence, we need to understand functions!
A function is a rule that assigns each input exactly one output.
(If you need to review the basics of functions, visit our lessons listed under Additional Resources in the right-hand sidebar.)
Let's say a function, or rule, is multiply by 9 and then subtract by 4. Whatever number we input into that function, we will get exactly one output.
For example, let's try 12:
For the input of 12, you will always get the output of 104 for this function.
You just evaluated a linear function!
Well, you could continue to input different numbers into the same function and calculate a set of output numbers. These sets can then become ordered pairs, and when graphed on a coordinate plane, they make a line.
Let's back up and look closer at this function.
The rule was multiply by 9 and then subtract by 4.
We can write that as an algebraic expression using x as our variable:
9x - 4
Now, we simply rewrite the expression using function notation. Since the rule is being performed on x, this function's output is dependent on the value of x. Also, this function will be named f.
Therefore, f(x) = 9x - 4
x being our input, or member of the domain, and the value of 9x - 4 being the output, or a member of the range.
f(12) = 9(12) - 4
f(12) = 104
x = 12 and f(x) = 104
Let's continue to build our domain and range sets:
Evaluate the function with a new input. Notice how the function, or rule, stays the same.
We can add this input and output to our domain and range sets:
Evaluate five more inputs.
Now, let's complete our function table:
The numbers in this function table are used to make ordered pairs:
(-7, -67) (0, -4) (1/3 , -1) (5, 41) (10, 86) (11, 95) (12, 104)
Any real number can be in the domain of this function; therefore, any number could be input as x and produce an output.
The function f(x) = 9x - 4 makes a line when graphed. It is written as the linear equation y = 9x - 4
Move on to the Got It? section to practice evaluating other types of functions.