1. Unit 3B Graph Radical Functions

2. Notice that the inverse of f(x) = x2 is not a function because it fails the vertical line test. However, if we limit the domain of f(x) = x2 to x ≥ 0, its inverse is the function
A radical function is a function whose rule is a radical expression. For example, we will study the square-root parent function and the cube-root parent function

3. Graph of Square Root Functionx y -1 i 1 4 2
Note: We cannot graph imaginary numbers on the coordinate plane. Therefore, the graph stops at x = 0.

4. Graph of the Cube Root x y -4 -1 1 4 1.59 -1.591 4
1.59
Note: Since the index number is odd, we can graph the function for all x values. Therefore, the domain is all reals.

5. Transformations of square root and cube root parent functions.
The general form of the square root function is
The cube root function is

6. Changing a a > 1 vertical stretch 0< a < 1 vertical shrink
a is - (flip vertically)

7. • • • • x (x, f(x)) Check It Out! Example 1b
Graph each function, and identify its domain and range. x
(x, f(x)) –1
(–1, 0) 3
(3, 2) 8
(8, 3) 15
(15, 4) • • • •
The domain is {x|x ≥ –1}, and the range is {y|y ≥0}.

8. Shift left h.
Shift right h.
Up k.
Down k.

9. Shift left h.
Shift right h.
Up k.
Down k.

10. Example 1 Solution Comparing Two Graphs h = -2 and k = -4
Describe how to create the graph of y = x – 4 from the graph of y = x .
Solution
h = -2 and k = -4
shift the graph to the left 2 units & down 4 units

11. v Example 2 Solution Graphing a Square Root Sketch the graph of
y = -3 x (dashed).
It begins at the origin and passes through point (1,-3).
Graphing a Square Root
Graph y = x –
(1, 3)
(0,0)
(2,0)
2) For y = -3 x – 1 + 3,
h = 1 & k = 3.
Shift both points 1 to the right and 3 up.
(1,-3)

12. Graphing a Square Root Graph y = 2 x – 2 + 1 . (3,3) (1,2) (2, 1)
(0,0)

13. v Example 3 Solution Graphing a Cube Root Sketch the graph of
y = 2 3 x (dashed).
It passed through the origin & the points
(1, 2) & (-1, -2).
Graphing a Cube Root
Graph y = 2 3 x + 3 – 4 .
(1, 2)
(0,0)
2) For y = 2 x + 3 – 4,
h = -3 & k = -4.
Shift the three points Left 3 and Down 4.
(-1,-2)
(-2,-2)
(-3,-4)
(-4,-6)

14. v Example 4
Using the graph of as a guide, describe the transformation and graph the function.
f(x)= x ●
g is f reflected across the y-axis and translated 3 units up.