Question
Which function is nonlinear
Y = 8 * 2x - 9 y = 5/8 x y equals 12x + 8 y = 5. (7.1)^2
Y = 8 * 2x - 9 y = 5/8 x y equals 12x + 8 y = 5. (7.1)^2
Answers
GPT-4o mini
To determine which of the given functions is nonlinear, we need to analyze each one:
1. **Y = 8 * 2^x - 9**: This is an exponential function because it involves \(2^x\), which means it is nonlinear.
2. **y = (5/8)x**: This is a linear function in the form \(y = mx + b\) (where \(m = 5/8\) and \(b = 0\)). Therefore, it is linear.
3. **y = 12x + 8**: This is also a linear function, as it follows the same format as the previous one.
4. **y = 5(7.1)^2**: This is a constant function since it simplifies to a constant value (it does not depend on \(x\)). However, constant functions are typically considered linear because they can be expressed in the linear form \(y = mx + b\) where \(m = 0\).
From the analysis above, the only nonlinear function listed is:
**Y = 8 * 2^x - 9**.
1. **Y = 8 * 2^x - 9**: This is an exponential function because it involves \(2^x\), which means it is nonlinear.
2. **y = (5/8)x**: This is a linear function in the form \(y = mx + b\) (where \(m = 5/8\) and \(b = 0\)). Therefore, it is linear.
3. **y = 12x + 8**: This is also a linear function, as it follows the same format as the previous one.
4. **y = 5(7.1)^2**: This is a constant function since it simplifies to a constant value (it does not depend on \(x\)). However, constant functions are typically considered linear because they can be expressed in the linear form \(y = mx + b\) where \(m = 0\).
From the analysis above, the only nonlinear function listed is:
**Y = 8 * 2^x - 9**.