Download N12-1-_Square_Root_and_Semi-Circle_Functions

N 12-1
Square Root and Semi-Circle Functions
The Square Root Parent Function
Graph
f(x) =
x
y
x
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
Domain: ____________
-10
Range: ____________
Characteristics:
Graph the following transformations of f(x). Check on your
calculator.
1. f(x) = x  5  3
2. f(x) = 2  x
Transformations:
Transformations:
10
y
10
8
8
6
6
4
4
2
y
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Domain: ______ Range: _______
4
6
8
10
Domain: ______ Range: _______
N 12-1
3. f(x) =  2x
Transformations:
10
4. f(x) = 5  x
Transformations:
y
10
8
8
6
6
4
4
y
2
2
x
x
-10
-8
-6
-4
-2
2
4
6
8
-10
10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Domain: ______ Range: _______
4
6
8
10
Domain: ______ Range: _______
Write the function for the following graphs.
5.
6.
10
y
10
8
8
6
6
4
4
2
y
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
4
6
8
10
N 12-1
Write the equation for a circle with center at (0, 0) and radius of 6
and then graph. Solve the equation for y.
10
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
-2
-4
-6
-8
-10
The Semi-Circle Parent Function
Graph
r 2  x2
f(x) =
x
Example: f(x) =
y
10
36  x 2
y
8
6
4
2
x
-10
-8
-6
-4
-2
2
-2
-4
Domain: ____________
Range: ____________
Characteristics:
-6
-8
-10
4
6
8
10
N 12-1
8. f(x) = 2 9  x 2
Transformations:
7. f(x) = 16  x 2  4
Transformations:
10
y
10
8
8
6
6
4
4
y
2
2
x
x
-10
-8
-6
-4
-2
2
4
6
8
-10
10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-6
-8
-8
-10
-10
Domain: ______ Range: _______
4
6
8
10
Domain: ______ Range: _______
Write the equation of the following functions.
9.
10.
10
y
10
8
8
6
6
4
4
2
y
2
x
-10
-8
-6
-4
-2
2
4
6
8
10
x
-10
-8
-6
-4
-2
2
-2
-2
-4
-4
-6
-8
-10
-6
-8
-10
4
6
8
10