1. Do Now: Write the recursive formula for the following problems or write the pattern. 1.a 1 = -3, a n = a n-1 +3 2. a 1 = -2, a n = 2a n-1 3.256, 64, 16, 4, 1 … 4. 3, 7, 11, 15, 19

2. Objective: To graph square root functions.

3. Vocab. A radical expression is an expression that contains a radical sign. If the radical is a square root then it’s called a square root function.

4. Parent Square Root Function:

5. EXAMPLE 1 SOLUTION STEP 1 Graph a function of the form y = a x Graph the function y = 3 x and identify its domain and range. Compare the graph with the graph of y = x. Make a table. Because the square root of a negative number is undefined, x must be nonnegative. So, the domain is x ≥ 0. STEP 2 Plot the points.

6. EXAMPLE 1 STEP 3 Graph a function of the form y = a x STEP 4 Draw a smooth curve through the points. From either the table or the graph, you can see the range of the function is y ≥ 0. Compare the graph with the graph of y = x. The graph of y = 3 x is a vertical stretch (by a factor of 3 ) of the graph of y = x.

7. EXAMPLE 2 Graph a function of the form y = a x SOLUTION Graph the function y = –0.5 x and identify its domain and range. Compare the graph with the graph of y = x. To graph the function, make a table, plot the points, and draw a smooth curve through the points. The domain is x ≥ 0. The range is y ≤ 0.The graph of y = –0.5 x is a vertical shrink (by a factor of 0.5 ) with a reflection in the x- axis of the graph of y = x.

8. EXAMPLE 3 Graph a function of the form y = x + k SOLUTION Graph the function y = x + 2 and identify its domain and range. Compare the graph with the graph of y = x. To graph the function, make a table, then plot and connect the points. The domain is x ≥ 0. The range is y ≥ 2.The graph of y = x + 2 is a vertical translation (of 2 units up) of the graph of y = x.

9. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 1. y = 2 x ANSWER Domain: x ≥ 0, Range: y ≥ 0 Vertical stretch by a factor of 2

10. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 2. y = x– 1 Domain: x ≥ 0, Range: y ≥ 0 – 1 Vertical translation of 1 unit down ANSWER

11. GUIDED PRACTICE for Examples 1, 2 and 3 Graph the function and identify its domain and range. Compare the graph with the graph of y = x. 3. y = x+ 3 Domain: x ≥ 0, Range: y ≤ 0 Vertical translation of 3 units up ANSWER

12. EXAMPLE 4 SOLUTION Graph a function of the form y = x – h Graph the function y = x – 4 and identify its domain and range. Compare the graph with the graph of y = x. To graph the function, make a table, then plot and connect the points. To find the domain, find the values of x for which the radicand, x – 4, is nonnegative. The domain is x ≥ 4.

13. EXAMPLE 4 Graph a function of the form y = x – h The range is y ≥ 0.The graph of y = x – 4 is a horizontal translation (of 4 units to the right) of the graph of y =. x

14. EXAMPLE 5 Graph a function of the form y = a x – h + k x + 4 Graph the function y = 2 – 1. SOLUTION STEP 1 Sketch the graph of y = 2. x STEP 2 So, h = –4 and k = –1. Shift the graph left 4 units and down 1 unit. y = 2 – 1 = 2 x – (–4) + (–1). x + 4 Shift the graph h units horizontally and k units vertically. Notice that

15. Exit Ticket for Examples 4 and 5 Graph the function y = x + 3 and identify its domain and range. Compare the graph with the graph of y = x. Domain: x ≥ – 3 ; Range: y ≥ 0 ; Horizontal translation 3 units to the left ANSWER

16. GUIDED PRACTICE for Examples 4 and 5 6. Identify the domain and range of the function in Example 5. The domain is x ≥ – 4. The range is y ≥ –1. ANSWER