5.7 Radical Functions
Objectives:
F.IF.7b: Graph square root, cube root, and piecewise-defined functions, including step
functions and absolute value functions,
F.BF.3: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for
specific values of k (both positive and negative); find the value of k given the graphs ….
For the board: You will be able to graph radical functions.
You will be able to transform radical functions by changing the parameters.
Anticipatory Set:
The square-root parent function is f(x) =
x
. The cube-root parent function is f(x) =
3x
.
Domain: {x|x ≥ 0} Domain: R
Range: {y|y ≥ 0} Range: R
The graphs of radical functions can be transformed .
x
0
1
4
y
0
1
2
x
0
1
8
-1
-8
y
0
1
2
-1
-2
Transformations of the Square-Root Parent Function f(x) =
x
Transformation
f(x) Notation
Example
Vertical translation
f(x) + k
y =
x
+ 3 3 units up
y =
x
- 4 4 units down
Horizontal translation
f(x + h)
y =
2x
2 units right
y =
1x
1 unit left
Vertical
stretch/compression
af(x)
y = 6
x
stretch by 6
y = ½
x
compress by ½
Horizontal
stretch/compression
f(bx)
y =
x
5
1
stretch by 5
y =
3x
compress by 1/3
Reflection
-f(x)
f(-x)
y = -
x
across x-axis
y =
x
across y-axis
