Let \( f(x)=2^{x} \) be the parent function. Let \( g(x)=2^{x-4} \) be a transformation of the parent function. Describe the change from the parent function. shift right 4 units shift up 4 units shift left 4 units shift down 4 units

The function \( g(x) = 2^{x-4} \) represents a horizontal shift of the parent function \( f(x) = 2^x \). Specifically, it shifts 4 units to the right. This transformation occurs because the input \( x \) is decreased by 4, meaning that for every input value, \( g(x) \) reaches its corresponding value from \( f \) at an input that is 4 units larger. In the context of transformations of functions, understanding shifts can help with problem-solving in algebra and calculus. One common mistake is to confuse shifts with reflections or stretches. Always remember: if you see a subtraction inside the function's argument (like \( x - 4 \)), that's a horizontal shift, while adding outside the function would be vertical shifts!