Nonlinear Relationship Math Example 3
Follow the full solution, then compare it with the other examples linked below.
Example 3
mediumFor \(y = x^2\), calculate values at \(x = -2, -1, 0, 1, 2\). Is the graph symmetric?
Solution
- 1 \(y(-2) = 4, y(-1) = 1, y(0) = 0, y(1) = 1, y(2) = 4\).
- 2 Points: \((-2,4),(-1,1),(0,0),(1,1),(2,4)\).
- 3 Yes — the graph is symmetric about the y-axis: \(f(-x) = f(x)\).
Answer
Values: 4,1,0,1,4; graph is symmetric about y-axis
\(y = x^2\) is an even function (\(f(-x)=f(x)\)), so it is symmetric about the y-axis.
About Nonlinear Relationship
A relationship between two quantities where the rate of change is not constant—the graph is curved, not a straight line.
Learn more about Nonlinear Relationship →More Nonlinear Relationship Examples
Example 1 medium
The area of a square is (A = x^2). Compare how (A) changes when (x) goes from 1 to 2, then 2 to 3. I
Example 2 hardFor (f(x) = x^2 - 4x + 3), find the vertex and determine whether the parabola opens up or down.
Example 4 hardDetermine whether (y = 2^x) is linear or nonlinear by examining the ratio (y_{n+1}/y_n) for (x = 0,