What is one effect of replacing with in the function when
? (1 point)
a reflection about the line
a shift to the right
a reflection about the -axis
a shift to the left

Replacing with where effectively introduces a twist to the function. Specifically, the negative flips the input values across the -axis. So, for , using mirrors the graph over the -axis, as all x-values become their opposites. This creates a reflective effect that can surprise anyone who doesn’t expect such a sudden change!

Now, let’s consider how this plays out with specific examples. If we take , substituting gives us . Compared to the original function, it’s inverted vertically as well as horizontally! It’s a fantastic lesson in how something simple like flipping a sign can lead to profound changes in a graph’s structure. Remember, a little algebra can lead to a lot of surprises!