BIG IDEAS MATH Let \( f(x)=2 x+3 \). Write a function \( g \) whose graph is a vertical stretch of the graph of \( f \) by a factor of 2 . The transformed function is \( g(x)=\square \)

To perform a vertical stretch of the graph of \( f(x) = 2x + 3 \) by a factor of 2, you multiply the entire function by 2. Therefore, the transformed function is \( g(x) = 2(f(x)) = 2(2x + 3) \), which simplifies to \( g(x) = 4x + 6 \). So, the transformed function is \( g(x) = 4x + 6 \). Imagine being able to stretch your favorite clothes! Just like fabric can be altered, functions can be modified too! With each stretch or compression, you're not just altering the shape; you're enhancing its characteristics, maintaining its essence while giving it a new flair. Functions reveal an intricate dance of numbers! Both the quadratic and linear transformations can guide real-world scenarios. For instance, if you were adjusting the dimensions of a greenhouse to ensure more sunlight reaches each plant, you'd essentially be applying the same concept: stretching your original design to maximize growth. Just like functions can be adjusted mathematically, so too can our designs in practical settings!