1. Section 10.1 Day 1 Square Root Functions
Algebra 1

2. Learning Targets Define square root function
Construct and identify the key characteristics of the parent square root function
Graph a square root function from a table using transformations
Identify the domain and range of a square root function

3. Group Discussion 𝒙 1 4 9 16 ? 𝐹(𝑥) 2 31 4 9 16 ?
𝐹(𝑥) 2 3
What are the next numbers in the table?
What is the explicit equation of the function?
𝐹 𝑥 =_________
Answer: 𝑥=25, 𝐹 𝑥 =5, 𝐹 𝑥 = 𝑥

4. A specific type of radical function
Square Root Function A function that contains the square root of a variable
A specific type of radical function
Example
𝑓 𝑥 = 𝑥−1 +4

5. Parent Square Root Function
Equation
𝑓 𝑥 = 𝑥
Table X Y 1 4 2 9 3

6. Parent Square Root Function
Graph
Domain
𝑥≥0
Range
𝑦≥0

7. Group Discussion
Given the graphs and their corresponding equations, what patterns can you conclude between the two?

8. Group Discussion
Given the graphs and their corresponding equations, what patterns can you conclude between the two?

9. Transformations General Form of a Square Root Function is 𝑦=𝑎 𝑥−ℎ +𝑘
𝑦=𝑎 𝑥−ℎ +𝑘
𝒉 represents
Horizontal Translation
(𝑥−ℎ): ℎ units to the R
𝑥+ℎ : ℎ units to the L
𝒌 represents
Vertical Translation
+𝑘: 𝑘 units up
−𝑘: 𝑘 units down
𝒂 represents
Dilation
Reflection
Of the variables 𝑥 and 𝑦, which variable does a horizontal shift impact? a vertical shift?

10. Graphing Procedure Identify the horizontal and vertical translations
Apply the translations to the parent square root function’s table
Graph the coordinate points
Identify the Domain & Range

11. Graphing: Example 1 Graph 𝑦= 𝑥+1
1. Horizontal Shift: Left 1, No Vertical Shift
2. Table
3. Graph −1, 0 , 0, 1 , 3, 2 , 8, 3
4. Domain: 𝑥≥−1, Range: 𝑦≥0 -1 X Y +0 1 3 4 2 8 9

12. Graphing: Example 2 Graph 𝑦=− 𝑥−3 −2 2. Table
1. Horizontal Shift: Right 3, Vertical Shift: Down 2
2. Table
3. Graph 3, −2 , 4, −1 , 7, 0 , (12, 1)
4. Domain: 𝑥≥3, Range: 𝑦≥−2 +3 X Y
∙−𝟏 -2 3 4 1 -1 -3 7 2 -4 12 9 -5

13. Graphing: Example 3 Graph 𝑦= 𝑥+4 +1 2. Table
1. Horizontal Shift: Left 4, Vertical Shift: Up 1
2. Table
3. Graph −4, 1 , −3, 2 , 0, 3 , 5, 4
4. Domain: 𝑥≥−4, Range: 𝑦≥1 -4 X Y +1 1 -3 2 4 3 5 9

14. Graphing: Example 4 Graph 𝑦= 𝑥 +3
1. No Horizontal Shift, Vertical Shift: Up 3
2. Table
3. Graph 0, 3 , 1, 4 , 4, 5 , (9, 6)
4. Domain: 𝑥≥0, Range: 𝑦≥3 +0 X Y +3 3 1 4 2 5 9 6