Question

Does the graph of the function y=3x−1−−−−√3
show that the function is increasing or decreasing?

Option 1: increasing

Option 2: decreasing

(1 point)

Answer 1

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

The function \( y = 3x - 1 - \sqrt{3} \) can be analyzed as follows:

1. **Identify the form of the function:**
The function is a linear equation in the form \( y = mx + b \), where \( m \) is the slope.

2. **Determine the slope (m):**
From the equation \( y = 3x - 1 - \sqrt{3} \), we can see that the coefficient of \( x \) (the slope \( m \)) is 3.

3. **Interpret the slope:**
- If \( m > 0 \), the function is increasing.
- If \( m < 0 \), the function is decreasing.

Since the slope \( m = 3 \) is positive, we can conclude that the function is **increasing**.

Therefore, the correct option is:

**Option 1: increasing**.