e) Write an equation for a function that has a graph with the given characteristics. The shape of \( y=\sqrt[3]{x} \) is shifted 1.1 units to the left. This graph is then vertically stretched by a factor of 8.7 . Finally, the graph is reflected across the \( x \)-axis.

Imagine starting with the original function \( y = \sqrt[3]{x} \). To shift it 1.1 units to the left, you would replace \( x \) with \( x + 1.1 \), giving you \( y = \sqrt[3]{x + 1.1} \). Next, apply the vertical stretch of 8.7 by multiplying the whole function by 8.7, resulting in \( y = 8.7\sqrt[3]{x + 1.1} \). Lastly, reflecting across the \( x \)-axis means you multiply the entire function by -1. So, the final equation is \( y = -8.7\sqrt[3]{x + 1.1} \). This describes a fascinating transformation journey of the cubic root function! Translations, stretches, and reflections not only alter the appearance of graphs but also give you insight into how functions can be manipulated in mathematics. The way these transformations work can inspire you to create unique pieces of mathematical art or models in real-world applications like engineering and physics!