Reflections by Christopher Monahan
The impact of a negative coefficient is to reflect the graph over an axis. Let the basic function be y = x2. Make the edited function y = -x2. Graph both functions. You can see that the edited function is reflected over the x-axis. y = x2 and y = |x| are both symmetric to the y-axis and do not illustrate an important transformation. Change the base function to
, and make the transformed function
. Graphing these functions illustrates once again that the graph of
y = -
f(
x) will be the reflection of
y =
f(
x) over the
x-axis. The domain for each of these functions is
x > 0, but the range changes. The range for
is
y > 0, whereas the range for
y = -
is
y < 0.
Change the transformed function to be
. The graph of
is reflected over the
y-axis, not over the
x-axis. The domain of
is
x > 0, whereas the range is
y > 0. The domain of
, whereas the range stays as
y > 0.
