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Building Functions from Context

Building Functions from Context. ~adapted from Walch Education. 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.

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Building Functions from Context

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  1. Building Functions from Context ~adapted from Walch Education

  2. 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

  3. 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.

  4. There’s more… • The 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.

  5. 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.

  6. 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) = 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) = a0b x. 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) = a1b x – 1. • A model can be used to analyze a situation.

  7. Thanks for watching! ~Dr. Dambreville

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