2. Building Functions from Context ~adapted from Walch Education

3. Don’t Forget to Take Notes… A situation that has a mathematical pattern can be represented using an equation. A variable is a letter used to represent an unknown quantity. An expression is a combination of variables, quantities, and mathematical operations. An equation is an expression set equal to another expression. An explicit equation describes the nth term in a pattern

4. And this… A linear equation relates two variables, and each variable is raised to the 1st power. The general equation to represent a linear function is f (x) = mx + b, where m is the slope and b is the y- intercept. An exponential equation relates two variables, and a constant in the equation is raised to a variable.

5. There’s more… The general equation to represent an exponential function is f (x) = ab x, where a and b are real numbers. Consecutive dependent terms in a linear function have a common difference. If consecutive terms in a linear pattern have an independent quantity that increases by 1, the common difference is the slope of the relationship between the two quantities.

6. It’s not over… Use the slope of a linear relationship and a single pair of independent and dependent values to find the linear equation that represents the relationship. Use the general equation f (x) = mx + b, and replace m with the slope, f (x) with the dependent quantity, and x with the independent quantity. Solve for b. Consecutive dependent terms in an exponential function have a common ratio.

7. Here’s the last of it… Use the common ratio to find the exponential equation that describes the relationship between two quantities. In the general equation f (x) = ab x, b is the common ratio. Let a 0 be the value of the dependent quantity when the independent quantity is 0. The general equation to represent the relationship would be: f (x) = a 0 b x. Let a 1 be the value of the dependent quantity when the independent quantity is 1. The general equation to represent the relationship would be: f (x) = a 1 b x – 1. A model can be used to analyze a situation.

8. Thanks for watching! ~Dr. Dambreville