Video Transcript
If the following graph is reflected
in the 𝑥-axis and then shifted to the left by one unit and down by three units,
what is the equation of the new graph?
The question describes three
transformations of the graph. The first is a reflection in the
𝑥-axis. In terms of transformations of
functions, this corresponds to multiplying a function by negative one. The second transformation is a
shift to the left by one unit. This transformation corresponds to
adding one to the argument of the function. The third transformation is a shift
down by three units. This corresponds to subtracting
three from the function.
We now apply these three
transformations in order to the function absolute value of 𝑥. First, we multiply by negative
one. Next, we add one to the
argument. Finally, we subtract three, giving
us the equation 𝑦 equals the negative absolute value of 𝑥 plus one minus
three.
