The transformation from \( y = 5^x \) to \( y = \frac{3}{4} \cdot 5^x \) involves a vertical compression.
To break it down:
- Original Function: \( y = 5^x \)
- 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 \( \frac{3}{4} \).