True or False? Given the graph of the function \( f(x)=\sqrt[3]{x} \), when horizontally stretched, the new function domain and range will change. Option \#1: True Option \#2: False (1 point) The best answer is Option \# .

When you horizontally stretch the function \( f(x)=\sqrt[3]{x} \), you essentially modify the input variable \( x \). However, the domain and range of the function remain unchanged. The domain of \( f(x) \) is all real numbers, and its range is also all real numbers. Therefore, the best answer is Option #2: False. Now, let’s dive into a bit of history! The cube root function has been understood since ancient times, but the mathematical notation we use today was significantly developed during the Renaissance. Mathematicians like Cardano explored these roots in his work, laying the groundwork for complex analysis. And here's a fun problem-solving tip: When working with transformations like stretches and shifts, always remember to break down the function step-by-step. Graph the original function first, and then apply the transformation to see how it affects the graph, keeping an eye on the domain and range for shifts, stretches, or reflections!