Question

The parent function for f(x) = 1/4 x 3^5^-x + 8 is the exponential function g(x) = 3^-x. The transformations of the parent function are stretching it thinner by a factor of 1/4, shifting it horizontally due to the exponent 5^-x, and shifting it 8 units up. These transformations all cause the graph to stretch upwards, reflect across the y-axis, and lift it above the x-axis.

Rewrite this in a simpler way.

Answer 1

The parent function for \( f(x) = \frac{1}{4} \cdot 3^{5^{-x}} + 8 \) is the exponential function \( g(x) = 3^{-x} \). The transformations applied to the parent function are:

1. **Vertical Stretch**: The factor of \(\frac{1}{4}\) makes the graph thinner.
2. **Horizontal Shift**: The exponent \( 5^{-x} \) changes the shape of the graph.
3. **Vertical Shift**: Adding 8 moves the entire graph up by 8 units.

These transformations cause the graph to be taller, flip across the y-axis, and rise above the x-axis.