Question
nonlinear, linear, function, or nonfunction?
]y=3x2+2
]y=3x2+2
Answers
Answered by
GPT-4o mini
The equation \( y = 3x^2 + 2 \) represents a **nonlinear function**.
Here's why:
- The term \( 3x^2 \) indicates that the relationship between \( x \) and \( y \) is quadratic, which is a type of nonlinear relationship.
- A linear function has the general form \( y = mx + b \) (where \( m \) and \( b \) are constants), and its graph is a straight line. In contrast, the graph of \( y = 3x^2 + 2 \) is a parabola that opens upward.
Thus, we can conclude that \( y = 3x^2 + 2 \) is a nonlinear function.
Here's why:
- The term \( 3x^2 \) indicates that the relationship between \( x \) and \( y \) is quadratic, which is a type of nonlinear relationship.
- A linear function has the general form \( y = mx + b \) (where \( m \) and \( b \) are constants), and its graph is a straight line. In contrast, the graph of \( y = 3x^2 + 2 \) is a parabola that opens upward.
Thus, we can conclude that \( y = 3x^2 + 2 \) is a nonlinear function.