Algebra 2: Section 7.5

Graphing Square Root and Cube Root Functions

Interval Notation (review)• Brackets mean > or < [ ]

• Parenthesis mean > or < ( )

3x 5x

15 7x

(3, )( , 5] [ 15,7]

( , )

Interval Notation

1x ( ,1) (1, )

Example: Find the inverse (review)

61. ( ) 729f x x

6729y x

6729x y6

729

xy

6

729

xy

6

3

xy

: [0, )D

6

6 729

xy

Square Root Function

y x

Square Root Function

1. 3y x 2. 3y x

• Shifted left 3 units • Shifted up 3 units

Square Root Function

3. 4y x 4. 2y x

• Shifted right 4 units • Shifted down 2 units

Domain and Range of Graphs

• Domain = x– What values of x

are part of the graph?

• Range = y– What values of y

are part of the graph? : [0, )Range

: [ 3, )Domain

Cube Root Function

3y x

:Domain:Range

( , ) ( , )

Rules for Graphing Cube & Square Roots

1. Sketch the graph of:

2.Shift h units horizontally and k units

vertically

3. What does the a do to the graph?

3ory a h hk y x kx a

3ory a x y a x

More Examples

35. 3 2

: : :V

x

R

y

D

6. 2 3 2

: : :V R

y x

D

(0,0)

(3,2)

(0,0)

( 3, 2) ( , ) ( , )

[3, ) [2, )

2 3 2?

What if the problem was

y x

3 3 2?

What if the problem was

y x

Reminder:1

2x

1

3x

x

3 x

1

22 3y x

1

31 2y x

2 3y x

3 1 2y x

Homework• P.434

#22-48 evens

• Use calculator to get general graph, then shift.– Sketch BOTH graphs using graph paper

• Must label the coordinate of the vertex of the graph.

• State the domain and range of each graph in interval notation!