Writing Function Rules

Dependent variable on the y-axis Independent variable on the x axis Graphs Dependent variable on the y-axis Independent variable on the x axis GPA Hours of Study a Week The graph above is a function of the GPA you might earn for a given amount of study each week. Discrete: the function is a collection of distinct values: i.e. 2, 3, 4, 5, …. with daily samples; etc Continuous: the function is unbroken over an interval: i.e. the GPA graph above

Major Strategies Try to digest one sentence at a time. Remember that not all sentences give formulas. Some just provide context. Write down your variables in a list, with what they mean Check if a formula is given to you in the problem statement. If so, start with that.

Look for words that suggest common formulas Using Known Formulas Look for words that suggest common formulas Profit: Profit = Income – Costs. Area: Any of a number of geometric formulas you have already learned: Rectangle: Area = length times width Triangle: Area = half the base times the height Circle: Area = pi times the radius squared Circumference: circumference = 2pi times the radius

Operation Phrases Less (more) than: Subtract (add) the previous number at the end. i.e “7 less than 2” = 2 – 7 Less (more): Subtract (add) the next number from the previous. i.e. “7 less 2” = 7 – 2 Each/every/per: Multiply the previous number with the variable that follows: “5 dollars per day (d)” = 5d Sum (difference): means to add (subtract) the terms in parenthesis: 5 times the sum of 6 and 7 = 5(6 + 7)

Using Units Often the units can tell you what operations to use. Example: You drive 60 mph for 3 hours how far do you go? Note: You want a distance (like miles). What you have is miles/hour. So, if you multiply by something in hours, you will be left with the miles that you want. In this case, 180 miles.

Summary Graphs of function rules Strategies for making function rules. Using formulas to make function rules Using key words to make function rules Using units to make function rules Thank you!