1. Lesson 13.3 graphing square root functions
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2. Square root functions Parent Function Standard Form 𝑦= 𝑥
𝑦= 𝑥
Standard Form
h = horizontal shift (h always wants to do the opposite)
𝑦=𝑎 𝑥−ℎ +𝑘
k = vertical shift
a = If a is positive, graph is above the x-axis
If a is negative, graph is reflected across the x-axis (below the x-axis)
If 𝑎 is greater than one, the graph has a stretch factor of 𝑎 .
If 𝑎 is less than one, the graph is compressed by a factor of 𝑎 .

3. Example 1- Graph each function by using a table and plotting points
Example 1- Graph each function by using a table and plotting points. State the direction of the shift from parent square root function, and by how many units. Then, state the domain and range.
−2+3 −2
(−2, −1)
1+3 −2
(1, 0)
6+3 −2
(6, 1)
13+3 −2
(13, 2)
Shifts –
Horizontal shift 3 units left, Vertical Shift 2 units down.
Domain – 𝑥≥−3
Range – y≥−2

4. Example 2- Graph each function by using a table and plotting points
Example 2- Graph each function by using a table and plotting points. State the direction of the shift from parent square root function, and by how many units. Then, state the domain and range.
−1+1
(−1, 0)
0+1
(0, 1)
3+1
(3, 2)
8+1
(8, 3)
Shifts –
Horizontal shift 1 unit left, no vertical shift.
Domain – 𝑥≥−1
Range – y≥0

5. Example 3- Graph each function by using a table and plotting points
Example 3- Graph each function by using a table and plotting points. State the direction of the shift from parent square root function, and by how many units. Then, state the domain and range.
(1, 1 2 )
(4,1)
(9, 1.5)
Shifts –
No horizontal or vertical shifts. Graph is compressed by a factor of 1 2
Domain – 𝑥≥0
Range – y≥0

6. Example 4- Graph each function by using a table and plotting points
Example 4- Graph each function by using a table and plotting points. State the direction of the shift from parent square root function, and by how many units. Then, state the domain and range.
3 1
(1,3)
3 4
(4,6)
3 9
(9, 9)
Shifts –
No horizontal or vertical shifts. Graph is stretched by a factor of 3.
Domain – 𝑥≥0
Range – y≥0

7. Example 5- Graph each function by using a table and plotting points
Example 5- Graph each function by using a table and plotting points. State the direction of the shift from parent square root function, and by how many units. Then, state the domain and range. −
(1,− 1 4 ) −
(4,− 1 2 ) −
(9, − 3 4 )
Shifts –
No horizontal or vertical shifts. Graph is compressed by a factor of And the graph is reflected across the x-axis
Domain – 𝑥≥0
Range – y≤0

8. Assignment #61
Pg. 647
3-14 all