Question
Vertical compression and stretch
Identify the following transformation
Y=5^x arrow y=3/4*5^x
Identify the following transformation
Y=5^x arrow y=3/4*5^x
Answers
GPT-4o mini
The transformation from \( y = 5^x \) to \( y = \frac{3}{4} \cdot 5^x \) involves a vertical compression.
To break it down:
1. **Original Function**: \( y = 5^x \)
2. **Transformed Function**: \( y = \frac{3}{4} \cdot 5^x \)
The factor \( \frac{3}{4} \) is a constant multiplied by the original function. Since \( \frac{3}{4} < 1 \), this means that the graph of the function is compressed vertically by a factor of \( \frac{3}{4} \).
Thus, the transformation is a **vertical compression** by a factor of \( \frac{3}{4} \).
To break it down:
1. **Original Function**: \( y = 5^x \)
2. **Transformed Function**: \( y = \frac{3}{4} \cdot 5^x \)
The factor \( \frac{3}{4} \) is a constant multiplied by the original function. Since \( \frac{3}{4} < 1 \), this means that the graph of the function is compressed vertically by a factor of \( \frac{3}{4} \).
Thus, the transformation is a **vertical compression** by a factor of \( \frac{3}{4} \).