Lesson 13.3 graphing square root functions Please tear out pages 641-652

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 .

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

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

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 2 1 (1, 1 2 ) 1 2 4 (4,1) 1 2 9 (9, 1.5) Shifts – No horizontal or vertical shifts. Graph is compressed by a factor of 1 2 Domain – 𝑥≥0 Range – y≥0

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

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 4 1 (1,− 1 4 ) − 1 4 4 (4,− 1 2 ) − 1 4 9 (9, − 3 4 ) Shifts – No horizontal or vertical shifts. Graph is compressed by a factor of 1 4 . And the graph is reflected across the x-axis Domain – 𝑥≥0 Range – y≤0

Assignment #61 Pg. 647 3-14 all