Does (x, y) satisfy the nonlinear function?

Learning Objectives Define what it means for an ordered pair to 'satisfy' a function. Accurately identify the x and y coordinates from a given point. Substitute the x and y values of a point into a nonlinear function's equation. Evaluate both sides of a nonlinear function equation after substitution using order of operations. Determine if the resulting numerical statement is true or false. Conclude whether a given point lies on the graph of a nonlinear function. Differentiate between linear and simple nonlinear function equations. Have you ever wondered if a specific location is on a curved path, like a roller coaster track or a rainbow? 🎢 Today, we'll learn how to mathematically check if a point 'fits' on a curved function! In this lesson,...

TermDefinitionExample Coordinate PlaneA two-dimensional surface formed by the intersection of a horizontal x-axis and a vertical y-axis, used to locate points.Plotting the point (3, 2) on a graph. Ordered Pair (x, y)A pair of numbers that represents a single point on the coordinate plane, where 'x' is the horizontal position and 'y' is the vertical position.In (5, -1), x = 5 and y = -1. FunctionA rule that assigns exactly one output value (y) for each input value (x).In $y = 2x + 1$, if $x=3$, then $y=7$. Nonlinear FunctionA function whose graph is not a straight line. Its equation often involves variables raised to powers other than 1 (like $x^2$ or $x^3$) or variables in denominators or under radicals.$y = x^2 - 4$ is a nonlinear function; its graph is a parabola. Sa...

Rule for Checking if a Point Satisfies a Function Substitute the $x$-coordinate into the $x$ variable of the function's equation and the $y$-coordinate into the $y$ variable. Then, evaluate both sides of the equation. If the left side of the equation equals the right side after substitution and evaluation, the point satisfies the function (and lies on its graph). If they are not equal, the point does not satisfy the function. General Form of Simple Nonlinear Functions (Examples) $y = ax^2 + bx + c$ (Quadratic), $y = ax^3 + b$ (Cubic), $y = a\sqrt{x}$ (Square Root) These are common forms of nonlinear functions you might encounter. The presence of $x^2$, $x^3$, or $\sqrt{x}$ (or similar operations) typically indicates a nonlinear relationship, meaning its graph will be cu...