Describe the transformation that takes f(x) = x + 1 to g(x) = -x + 4

For this case we have the following function:   f (x) = x + 1  we apply the following transformations:   reflections:   to graph y = f (-x), reflect the graph of y = f (x) on the y-axis. (horizontal reflection)  we have then:   h (x) = -x + 1  vertical translations  suppose that k> 0  to graph y = f (x) + k, move the graph of k units up.  we have entoces:   g (x) = -x + 1 + 3  g (x) = -x + 4  answer:   reflection on the y axis.  displacement 3 units up.

The transformation will be a reflection across the y-axis followed by a translation 5 units up. explanation: in order to make x negative, we reflect the equation across the y-axis. this makes g(x)=-f(x); g(x)=-(x+1) = -x-1. we want to add 4 to -x instead of subtract 1. this means we must add 5 to our function: g(x)=-x-1+5=-x+4. adding 5 to the end is a vertical translation 5 units up.