Question

Analyze the graphs of f(x)=|x|
and g(x)=|3.5x|
. Which statement correctly describes the domain and range changes, if any, from f(x) to g(x)?(1 point)
Responses

The domain and range both change to [3.5,∞).
The domain and range both change to [3.5,∞).

The domain changes to [3.5,∞).
The domain changes to [3.5,∞).

The range changes to [3.5,∞).
The range changes to [3.5,∞).

The domain and range stay the same.
The domain and range stay the same.

Answer 1

To analyze the functions \( f(x) = |x| \) and \( g(x) = |3.5x| \), let’s first determine their domains and ranges.

1. **Domain**:
- The domain of \( f(x) = |x| \) is all real numbers, denoted as \( (-\infty, \infty) \).
- The domain of \( g(x) = |3.5x| \) is also all real numbers, denoted as \( (-\infty, \infty) \).

**Conclusion**: The domain does not change; it remains \( (-\infty, \infty) \) for both functions.

2. **Range**:
- The range of \( f(x) = |x| \) is all non-negative real numbers, denoted as \( [0, \infty) \).
- The range of \( g(x) = |3.5x| \) is also all non-negative real numbers, denoted as \( [0, \infty) \).

**Conclusion**: The range does not change; it remains \( [0, \infty) \) for both functions.

Based on the analysis, both the domain and range of \( f(x) \) and \( g(x) \) remain the same.

### Correct Statement:
**The domain and range stay the same.**