Section 10.1 Day 1 Square Root Functions Algebra 1

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

Group Discussion 𝒙 1 4 9 16 ? 𝐹(𝑥) 2 3 1 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

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

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

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

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

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

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?

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

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

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

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

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