Section 6.5Graph Square Root and Cube Root Functions

Radical Functions

•Review:•y = √x & y = 3√x

•New:•y =a √(x-h) + k & y = a3 √(x – h) +

k

Parent Function: y = √x

•Domain: x > 0

•Range: y > 0

Parent Function: y = 3√x

•Domain: all real numbers•Range: all real numbers

Translations and Shifts

•a & k change the y-value▫Take the original y-value

a(y) + k

•h changes the x-value▫Take the original x-value

x + h

y =a √(x-h) + k& y = a3√(x – h) + k

EXs.• y = 2 √x + 2

Change the y:▫Double it and add 2

• y = -1 √(x – 1) – 3 Change the y:

Take the opposite and subtract 3

Change the x: Add 1

Points of Importance: y = √x x 0 1 4 9

y 0 1 2 3

Points of Importance: y = 3√x x 0 1 8 -1 -8

y 0 1 2 -1 -2

EX. y = 2 √(x – 1) + 3

•Now Plot!

x 0 1 4 9

y 0 1 2 3

New x: x + 1

1 2 5 10

New y: 2y + 3

3 5 7 9

Now Graph…

Ex. y = -33√(x + 7) - 6x 0 1 8

y 0 1 2

New x: x - 7 -7 -6 1

New y: -3y - 6

-6 -9 -12

Note:

•Label the parent and translation.•Make the parent graph be the dashed

curve.•Show the table of values.

Your Turn:

•449•A:3,7,11,17,19,29,41,43•B:6,10,16,32,44,47•C:5,15,19,20,30,50