Does (x, y) satisfy the nonlinear function?

Learning Objectives Define what a nonlinear function is and provide examples. Correctly identify the x and y coordinates from an ordered pair. Substitute the coordinates of a point into a given nonlinear function's equation. Evaluate both sides of the equation after substitution using the order of operations. Determine whether the substituted values make the function's equation a true or false statement. Explain what it means for a point to 'satisfy' a nonlinear function. Distinguish between linear and simple nonlinear function equations. Have you ever wondered if a specific location is 'on the path' of a roller coaster? 🎢 Today, we'll learn how to check if a point is 'on the graph' of a special type of function! In this lesso...

TermDefinitionExample Nonlinear FunctionA function whose graph is not a straight line. Its equation often involves variables raised to powers other than 1 (like x²) or inside absolute value symbols.The function y = x² is nonlinear because its graph is a curve (a parabola). Ordered Pair (x, y)A pair of numbers used to locate a point on a coordinate plane. The first number (x) is the horizontal position, and the second number (y) is the vertical position.The ordered pair (3, 9) represents a point where x = 3 and y = 9. Satisfy an EquationWhen the values of the variables in an equation make the equation a true statement. If a point (x, y) satisfies a function, it means the point lies on the graph of that function.The point (2, 4) satisfies the equation y = x + 2 because 4 = 2 + 2 is true. Su...

The Point-Satisfaction Rule A point (x, y) satisfies a function if, when its x and y values are substituted into the function's equation, the equation becomes a true statement. This rule tells us the fundamental condition for a point to be 'on' the graph of a function. If the equation holds true, the point is on the graph. Substitution Principle To check if (x, y) satisfies a function, replace every 'x' in the function's equation with the x-coordinate of the point, and replace every 'y' with the y-coordinate of the point. This is the first step in the process. Make sure to substitute the correct value for the correct variable. Evaluation Principle After substitution, simplify both sides of the equation using the order of operatio...