Practice Nonlinear Relationship in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
A relationship between two quantities where the rate of change is not constant—the graph is curved, not a straight line.
Not a straight line—it curves. Compound interest grows faster and faster.
Example 1
mediumThe area of a square is \(A = x^2\). Compare how \(A\) changes when \(x\) goes from 1 to 2, then 2 to 3. Is this relationship linear?
Example 2
hardFor \(f(x) = x^2 - 4x + 3\), find the vertex and determine whether the parabola opens up or down.
Example 3
mediumFor \(y = x^2\), calculate values at \(x = -2, -1, 0, 1, 2\). Is the graph symmetric?
Example 4
hardDetermine whether \(y = 2^x\) is linear or nonlinear by examining the ratio \(y_{n+1}/y_n\) for \(x = 0, 1, 2, 3\).