Transcript 7.5 Graphs Radical Functions

7.5 Graphs Radical Functions
Graph of the Square Root
x
-1
0
1
4
x
y x
y
i
0
1
2
Note: We cannot graph
imaginary numbers on
the coordinate plane.
Therefore, the graph
stops at x = 0.
5
4
3
2
1
-5
-4
-3
-2
-1

-1
-2
-3
-4
-5


1
2
3
4
5
Graph of the Cube Root
x
-4
-1
0
1
4
3
x
y x
3
y
-1.59
-1
0
1
1.59
Note: Since the index
number is odd, we can
graph the function for all
x values. Therefore, the
domain is all reals.
55
44
33
22
11
-5
-5 -4
-4 -3
-3 -2
-2 -1
-1



-1
-1
-2
-2
-3
-3
-4
-4
-5
-5


11
22
33
4
5
The General Equation
The general form of the square root function is
y  a xh k
The cube root function is
y  a3 x h k
y  a xh k
f ( x)  x
Add a positive positive
number to x.
f ( x)  x  h
Shift left h.
Add a negative number
to x.
f ( x)  x  h
Shift right h.
Add a positive
Add a negative
number to the radical. number to the radical.
f ( x)  x  k
Up k.
f ( x)  x  k
Down k.
y  a xh k
3
f ( x)  3 x
Add a positive positive
number to x.
f ( x)  3 x  h
Shift left h.
Add a negative number
to x.
f ( x)  3 x  h
Shift right h.
Add a positive
Add a negative
number to the radical. number to the radical.
f ( x)  3 x  k
Up k.
f ( x)  3 x  k
Down k.
Changing a
10
8
6
4
2
f ( x)  x
3
a is greater than 1
f ( x)  4 x
3
a is greater than 0
and less than 1.
13
f ( x) 
x
2
a is less than 0.
f ( x )  1 3 x
-10 -8
-6
-4
-2
-2
-4
-6
-8
-10
2
4
6
8
10
Problems
Describe how to obtain the graph of g from the
graph of f.
g ( x)  x  5
f ( x)  x
Shift left 5 units.
g ( x )   3 x  10
f ( x)  3 x
Reflect in y = 0, shift down
10 units.
Problems
State the domain and range.
f ( x)  x  6
x > -6, y > 0
f ( x )  3 3 x  7  4
x, y all real numbers