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Do Now:

Do Now:. Write the recursive formula for the following problems or write the pattern. a 1 = -3, a n = a n-1 +3 a 1 = -2, a n = 2a n-1 256, 64, 16, 4, 1 … 3, 7, 11, 15, 19. Objective:. To graph square root functions. Vocab.

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Do Now:

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  1. Do Now: Write the recursive formula for the following problems or write the pattern. • a1= -3, an = an-1 +3 • a1= -2, an = 2an-1 • 256, 64, 16, 4, 1 … • 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. Graph a function of the form y = a x EXAMPLE 1 Graph the function y = 3 xand identify its domain and range. Compare the graph with the graph of y = x. SOLUTION Make a table. Because the square root of a negative number is undefined, x must be nonnegative. So, the domain is x ≥ 0. STEP 1 Plot the points. STEP 2

  6. Graph a function of the form y = a x Compare the graph with the graph of y = x. The graph ofy = 3 xis a vertical stretch (by a factor of 3) of the graph of y = x. EXAMPLE 1 STEP 3 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. STEP 4

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

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

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

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

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

  12. Graph a function of the form y = x – h EXAMPLE 4 Graph the function y = x – 4 and identify its domain and range. Compare the graph with the graph of y = x. SOLUTION 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. x 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 = . EXAMPLE 4 Graph a function of the form y = x – h

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

  15. ANSWER for Examples 4 and 5 Exit Ticket 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

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

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