A function is defined as linear if it can be expressed in the form \( f(x) = mx + b \), where \( m \) and \( b \) are constants. Functions that do not fit this form, such as quadratic functions, exponential functions, or any functions whose graphs are not straight lines, are considered nonlinear.
Here are some examples of equations that define functions which are not linear:
- Quadratic Function: \( f(x) = ax^2 + bx + c \) (where \( a \neq 0 \))
- Cubic Function: \( f(x) = ax^3 + bx^2 + cx + d \) (where \( a \neq 0 \))
- Exponential Function: \( f(x) = a \cdot b^x \) (where \( b > 0 \) and \( b \neq 1 \))
- Trigonometric Function: \( f(x) = \sin(x) \) or \( f(x) = \cos(x) \)
These types of functions exhibit curves or shapes that are not a straight line, thus making them non-linear. If you provide specific equations, I can help identify which ones are not linear.