Evaluate a nonlinear function

Learning Objectives Define what a nonlinear function is and distinguish it from a linear function. Identify the input (domain) and understand its role in a function. Accurately substitute numerical values into nonlinear function expressions. Apply the order of operations (PEMDAS/BODMAS) to correctly evaluate expressions. Calculate the output (range) of a nonlinear function for a given input. Interpret the result of a function evaluation as a point on its graph. Ever wondered how roller coasters are designed to have exciting curves, not just straight lines? 🎢 Functions help us understand these curved paths! In this lesson, you'll learn how to 'evaluate' nonlinear functions. This means you'll take a number, put it into a function's rule, and find out...

TermDefinitionExample FunctionA rule that assigns exactly one output value for each input value.If you input a number, the function might square it. For $f(x) = x^2$, an input of 3 gives an output of 9. Nonlinear FunctionA function whose graph is not a straight line. Its rule often involves variables raised to powers other than 1 (like $x^2$ or $x^3$), or variables in the denominator, or under a square root.$f(x) = x^2$ is a nonlinear function because its graph is a parabola (a curve). Input (Domain)The value that you substitute into the function. It's usually represented by a variable like $x$ or $t$.In $f(x) = x^2 + 5$, if you want to find $f(-3)$, then $-3$ is the input. Output (Range)The result you get after evaluating the function with a specific input. It's usually represe...

Function Notation $f(x)$ represents the output of a function named $f$ when the input is $x$. This notation tells you what variable to substitute for and that the result is the function's value at that input. For example, $f(3)$ means 'evaluate function $f$ when $x=3$.' Substitution Principle To evaluate $f(a)$, replace every instance of the variable $x$ in the function's expression with the specific numerical input $a$. This is the first step in finding the output. Always use parentheses around the number you are substituting, especially if it's negative or involves exponents, to avoid errors. Order of Operations (PEMDAS/BODMAS) 1. Parentheses/Brackets 2. Exponents/Orders 3. Multiplication and Division (from left to right) 4. Addition and Subt...