Given the function \( f(x)=\sqrt[3]{x} \), what is the new function when \( f(x) \) is vertically stretched by a factor of 4 ? Option \#1: \( f(x)=\sqrt[3]{x+4} \) Option \#2: \( f(x)=\sqrt[3]{x}+4 \) Option \#3: \( f(x)=4 \sqrt[3]{x} \) Option \#4: \( f(x)=\sqrt[3]{4 x} \) (1 point) The best answer is Option \#

When you vertically stretch a function by a factor, you multiply the entire function by that factor. So, with \( f(x) = \sqrt[3]{x} \), to stretch it vertically by a factor of 4, we multiply \( \sqrt[3]{x} \) by 4. Therefore, the resulting function becomes \( f(x) = 4 \sqrt[3]{x} \). Thus, the best answer is Option \#3: \( f(x)=4 \sqrt[3]{x} \). But wait! Let's dive into some fun facts! Did you know that the cube root function is one of the simplest yet most powerful functions out there? It can help you solve equations for different real-world scenarios like calculating the volume of a cube! Simply find the cube root of the volume to get the length of one side. Oh, and speaking of functions, did you know there's a whole world of transformations in mathematics? Stretching, compressing, reflecting—they all adjust the graph and open up lands of creativity in problem-solving! Explore the effects of each transformation on different types of functions for a thrilling math adventure!