To determine if an equation defines a function that is not linear, we need to understand what a linear function is. A linear function can be expressed in the form \(y = mx + b\), where \(m\) and \(b\) are constants. Linear functions produce graphs that are straight lines.
Non-linear functions may include:
- Quadratic functions (e.g., \(y = ax^2 + bx + c\))
- Cubic functions (e.g., \(y = ax^3 + bx^2 + cx + d\))
- Exponential functions (e.g., \(y = a \cdot b^x\))
- Trigonometric functions (e.g., \(y = \sin(x)\))
- Any equation that involves absolute values, square roots, etc., that does not simplify to the linear form.
If you have a list of equations you would like to evaluate, please provide them so that I can help identify which one is not linear.
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