Question

If I have a function such as f(x) = -2x+1, which of the following statements is true?

a.
The function is a decreasing function.

b.
The function is an increasing function.

c.
The function is a constant function.

d.
It is not a function.

Answer 1

To determine the nature of the function \( f(x) = -2x + 1 \), let's analyze its characteristics:

1. **Slope**: The function is a linear function in the form \( f(x) = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept. Here, \( m = -2 \).

2. **Increasing or Decreasing**:
- If the slope (\( m \)) is positive, the function is increasing.
- If the slope (\( m \)) is negative, the function is decreasing.
- If the slope is zero, the function is constant.

Since the slope \( m = -2 \) is negative, the function is a decreasing function.

Based on this analysis, the true statement is:

**a. The function is a decreasing function.**