Evaluate a nonlinear function

Learning Objectives Define what a nonlinear function is and distinguish it from a linear function. Identify the input (independent variable) and output (dependent variable) in a given function. Accurately substitute numerical values for the independent variable into a nonlinear function's equation. Apply the order of operations (PEMDAS/BODMAS) correctly to simplify expressions within nonlinear functions. Calculate the output (function value) for a given input in various nonlinear functions. Express the evaluation of a nonlinear function using standard function notation. Ever wonder how rollercoasters are designed or how a ball flies through the air? 🎢 These movements aren't straight lines; they follow curves described by special mathematical rules! In this lesson...

TermDefinitionExample FunctionA rule that assigns exactly one output value to each input value. Think of it like a machine: you put something in, and it gives you exactly one thing out.The function $f(x) = 2x + 1$ takes an input $x$ and gives an output $2x+1$. For $x=3$, the output is $2(3)+1=7$. Nonlinear FunctionA function whose graph is not a straight line. Its equation often involves variables raised to powers other than 1 (like $x^2$, $x^3$) or variables in the denominator.$f(x) = x^2$ is a nonlinear function because its graph is a curve (a parabola). Input (Independent Variable)The value that is substituted into the function. It's the 'cause' or the value you choose. It's typically represented by $x$ or another letter like $t$ for time.In $f(x) = x^2 + 5$, if we...

Function Notation $f(x) = \text{expression involving } x$ This notation represents a function where $x$ is the input (independent variable) and $f(x)$ is the output (dependent variable). Other letters like $g(t)$ or $h(z)$ can also be used. Evaluating a Function To evaluate $f(x)$ at $x=a$, substitute $a$ for every $x$ in the expression: $f(a) = \text{expression with } a \text{ substituted for } x$. This rule tells you exactly how to find the output for a given input. Replace all instances of the variable with the specific number and then simplify using the order of operations. Order of Operations (PEMDAS) $P \rightarrow E \rightarrow MD \rightarrow AS$ Always follow this order when simplifying expressions: Parentheses first, then Exponents, then Multiplication and D...