Building Functions from Context

Building Functions from Context~adapted from Walch Education

Dont Forget to Take NotesA 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 patternAnd thisA 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.

Theres moreThe general equation to represent an exponential function is f(x) = abx, 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.

Its not overUse 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.

Heres the last of itUse the common ratio to find the exponential equation that describes the relationship between two quantities. In the general equation f(x) = abx, b is the common ratio. Let a0 be the value of the dependent quantity when the independent quantity is 0. The general equation to represent the relationship would be: f(x) = a0bx. Let a1 be the value of the dependent quantity when the independent quantity is 1. The general equation to represent the relationship would be: f(x) = a1bx 1.A model can be used to analyze a situation.

Thanks for watching!~Dr. Dambreville