6-8
Graphing Radical Functions
(Half-Graphs)
A radical equation defines a radical function.
f(x) = √x
Translations:
Vertical: The graph of the radical function
y = √x +k is a translation of y = √x up k
units if k is positive and down if k is
negative.
Ex: y = √x +2
Graph
Horizontal Translations:
The graph of y = √(x –h) is a translation of
y = √x shifted h units to the right if h is
positive and h units to the left if h is
negative. (You always do the opposite)
Ex. y = √(x-2)
The graph of y = a√x is a vertical stretch or
compression of the graph of y = √x by a
factor of a. If a<0, the graph is a reflection
across the x axis.
Ex. y = -√x
Other equations
y = x3
and
y = 3 √x
The translations work the same way.
Opposite if in the x direction, the same if in
the y direction.
You need to memorize these!!!
Graph:
y= 3 √(x+5)
and
y = 3 √x +5
Hw pg 418 7-20 25-30 all