4.A A point and its reflection over a line are both
equidistant to that line. Imagine that point Qhas
a ycoordinate of 4 (any value between 1 and 6 will
do). This implies that point Qis two units from the
line y= 6, and therefore, point Palso must be two
units from the line y= 6 and must have a ycoordi-
nate of 8. Point Qalso must be three units from
the line y= 1, so point Ralso must be three units
from the line y= 1 and must have a ycoordinate
of 2. Therefore, the length of PRis 8 (2) = 10.
CHAPTER 11 / ESSENTIAL ALGEBRA 2 SKILLS 421
5.E You can determine the equation defining the
function through substitution: y=g(f(h(x))) =
g(f(x^2 )) = g(x^2 + 1)) = x^2 1, which describes an
“open-down” parabola with vertex at (0, 1).
Notice that this sequence of transformations takes
the standard parabola y= x^2 and shifts it up one
unit and then reflects the new graph over the
x-axis.