Video Transcript
Which of the following processes
would you use to obtain the graph of 𝑦 equals negative 𝑓 of negative 𝑥 from the
graph of 𝑦 equals 𝑓 of 𝑥? Is it (a) reflect the graph in the
𝑥-axis? (b) Reflect the graph in the
𝑦-axis. Is it (c) reflect the graph in the
line 𝑦 equals 𝑥? Or (d) reflect the graph in the
line 𝑦 equals negative 𝑥.
So let’s think about the processes
or the transformations that would map the graph 𝑦 equals 𝑓 of 𝑥 onto the graph 𝑦
equals negative 𝑓 of negative 𝑥. Suppose we have the graph of some
function 𝑦 equals 𝑓 of 𝑥. To obtain the graph of 𝑦 equals 𝑓
of negative 𝑥, we need to reflect the graph of the original function in the
𝑦-axis. So looking at the graph on our
coordinate plane, 𝑦 equals 𝑓 of negative 𝑥 would look like this.
But the graph of 𝑦 equals negative
𝑓 of 𝑥 would be obtained by reflecting the graph of 𝑦 equals 𝑓 of 𝑥 in the
𝑥-axis. So it might look a little something
like this. Now we have 𝑦 equals negative 𝑓
of negative 𝑥. So that tells us it’s going to be a
combination of the two reflection. But in fact, when we are
reflecting, it doesn’t matter the order in which we do it. So we could reflect across the
𝑥-axis and then across the 𝑦-axis or across the 𝑦-axis then across the
𝑥-axis. Either way, we obtain the graph of
𝑦 equals negative 𝑓 of negative 𝑥 from the graph of 𝑦 equals 𝑓 of 𝑥 by
reflecting the graph in the 𝑥-axis and in the 𝑦-axis. So the answer is (a) and (b).
