Question

Does the graph of the function y = 3x−1−−−−√3
show that the function is increasing or decreasing. (1 point)
Responses

increasing
increasing

decreasing
decreasing

neither, it is constant

Answer 1

To analyze whether the function \( y = \sqrt{3}(3x - 1) \) is increasing or decreasing, we can look at its derivative.

1. **Find the derivative**: The function can be expressed as \( y = \sqrt{3}(3x - 1) \). To find the derivative:

\[
\frac{dy}{dx} = \sqrt{3} \cdot 3 = 3\sqrt{3}
\]

2. **Analyze the derivative**: The derivative \( 3\sqrt{3} \) is a positive constant.

Since the derivative is positive, this means that the function is **increasing** everywhere.

Therefore, the correct answer is:

**increasing**.