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Warm Up

Graph Square Root Functions. Warm Up. Lesson Presentation. Lesson Quiz. 3. Evaluate x + 5 when x = 11. √. ANSWER. √. 2. Evaluate 3 x when x = 4. 6. 4. ANSWER. ANSWER. Warm-Up. 1. Graph the function y = 2 x. Example 1.

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Warm Up

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  1. Graph Square Root Functions Warm Up Lesson Presentation Lesson Quiz

  2. 3.Evaluate x + 5 when x=11. √ ANSWER √ 2.Evaluate 3x when x=4. 6 4 ANSWER ANSWER Warm-Up 1.Graph the functiony = 2x.

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

  4. 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 4

  5. 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 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.

  6. 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 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.

  7. ANSWER 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

  8. ANSWER Guided Practice Graph the functionand identify its domain and range. Compare the graph with the graph of y = x. y = –2 2. x Domain: x ≥ 0, Range: y ≤ 0 Vertical stretch by a factor of 2 and a reflection in the x-axis

  9. ANSWER Guided Practice Graph the functionand identify its domain and range. Compare the graph with the graph of y = x. y = 3. x – 1 Domain: x ≥ 0, Range: y ≥ 0 – 1 Vertical translation of 1 unit down

  10. ANSWER Guided Practice Graph the functionand identify its domain and range. Compare the graph with the graph of y = x. y = 4. x + 3 Domain: x ≥ 0, Range: y ≤ 0 Vertical translation of 3 units up

  11. x – 4 Example 4 Graph the function y = 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.

  12. 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

  13. 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 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.

  14. ANSWER ANSWER The domain is x ≥ – 4. The range isy ≥ –1. Guided Practice 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 6. Identify the domain and range of the function in Example 5.

  15. x + 2.2 The graph of the function is shown. Using the trace feature, you can see that y 325 when x = 10. So, microphone sales were about $325 million 10 years after 1988, or in 1998. Example 6 MICROPHONE SALES For the period 1988–2002, the amount of sales y(in millions of dollars) of microphones in the United States can be modeled by the functiony = 93where xis the number of years since 1988. Graph the function on a graphing calculator. In what year were microphone sales about $325 million? SOLUTION

  16. ANSWER 1993 Guided Practice 7. MICROPHONE SALES:Use the function in Example 6 to find the year in which microphone sales were about $250 million.

  17. 1. Graph the function y = 2 x + 1. ANSWER Lesson Quiz

  18. ANSWER 1 2 Lesson Quiz 2. Graph the function y = x – 2 + 1.

  19. ANSWER 1 4 1296 ft Lesson Quiz 3. Graph the function t = h, where t is time (in seconds) and h is distance (in feet) to model a sky diver’s freefall. How many feet did a sky diver freefall if the freefall lasted 9 seconds?

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