Whte the equation of a function whose parent function, \( f(x)=x+5 \), is shifted 3 units to the right. \( O g(x)=x+3 \) \( O g(x)=x+8 \) \( O g(x)=x-8 \) \( O g(x)=x+2 \)

To shift the parent function \( f(x) = x + 5 \) 3 units to the right, you adjust the input \( x \) to \( x-3 \). Therefore, the new function becomes \( g(x) = (x-3) + 5 \), which simplifies to \( g(x) = x + 2 \). So the correct option is \( g(x) = x + 2 \). Now, for more fun facts: When you shift a function to the right, you're basically delaying its output! Just imagine you're giving the function a little vacation from its original position—it gets to relax before reacting to the input. A common mistake in function transformations is mixing up horizontal and vertical shifts. Remember: shifting to the right involves subtracting from the input inside the function, while shifting up simply adds to the output! So next time you're shifting functions, keep that straight!