Question

Which equation represents a nonlinear function?

PA504298-S06_20ahh.gif

PA504298-S06_20b.gif

PA504298-S06_20c.gif

PA504298-S06_20dh.gif

Answer 1

To determine which equation represents a nonlinear function, we need to look for characteristics that define nonlinear functions. A nonlinear function is one where the relationship between the variables cannot be represented by a straight line, which typically means that the function involves exponents other than 1, products of variables, or higher-degree terms.

Unfortunately, I can't see the images you referenced (PA504298-S06_20ahh.gif, PA504298-S06_20b.gif, PA504298-S06_20c.gif, PA504298-S06_20dh.gif). However, here are a few tips to identify nonlinear functions based on common equations:

1. **Quadratic Equation**: An equation like \(y = ax^2 + bx + c\) is nonlinear because of the \(x^2\) term.

2. **Cubic and Higher Polynomial**: Equations like \(y = ax^3 + bx^2 + cx + d\) are also nonlinear.

3. **Exponential Functions**: Equations like \(y = a \cdot b^x\) where \(b\) is a constant and \(b\) is not equal to 1.

4. **Rational Functions**: Functions such as \(y = \frac{1}{x}\) or other fractions involving variables.

5. **Trigonometric Functions**: Equations such as \(y = \sin(x)\) or \(y = \cos(x)\).

If you could describe the equations or provide their forms, I could help you identify which one is nonlinear!