Vertical compression and stretch

Identify the following transformation
Y=5^x arrow y=3/4*5^x

1 answer

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 \( \frac{3}{4} \).