Question
Which equation represents a nonlinear function
y=1/2x-7
y=x2^+4
y=(3 4^)x-2
y=5x+3 2^
y=1/2x-7
y=x2^+4
y=(3 4^)x-2
y=5x+3 2^
Answers
Answered by
GPT-4o mini
To determine which equation represents a nonlinear function, we need to analyze the provided equations:
1. **y = (1/2)x - 7**: This is a linear equation (it has the form y = mx + b), which graphically represents a straight line.
2. **y = x^2 + 4**: This is a quadratic equation because of the \(x^2\) term. This represents a parabola, which is a nonlinear function.
3. **y = (3 * 4^x) - 2**: This can be simplified to represent an exponential function as \(y = 3 * 4^x - 2\). Exponential functions are nonlinear.
4. **y = 5x + 3 * 2^1**: This can be simplified to \(y = 5x + 3 * 2\), which is also a linear function, as it represents a straight line.
Thus, the equations that represent nonlinear functions are:
- **y = x^2 + 4**
- **y = (3 * 4^x) - 2**
The only explicitly nonlinear function in a conventional context from your examples is **y = x^2 + 4**.
1. **y = (1/2)x - 7**: This is a linear equation (it has the form y = mx + b), which graphically represents a straight line.
2. **y = x^2 + 4**: This is a quadratic equation because of the \(x^2\) term. This represents a parabola, which is a nonlinear function.
3. **y = (3 * 4^x) - 2**: This can be simplified to represent an exponential function as \(y = 3 * 4^x - 2\). Exponential functions are nonlinear.
4. **y = 5x + 3 * 2^1**: This can be simplified to \(y = 5x + 3 * 2\), which is also a linear function, as it represents a straight line.
Thus, the equations that represent nonlinear functions are:
- **y = x^2 + 4**
- **y = (3 * 4^x) - 2**
The only explicitly nonlinear function in a conventional context from your examples is **y = x^2 + 4**.