Section 6.5 Graph Square Root and Cube Root Functions.
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Transcript of Section 6.5 Graph Square Root and Cube Root Functions.
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