1 / 11

EXAMPLE 4

b. Write a power function y = ax whose graph passes through (3, 2) and (6, 9). Substitute the coordinates of the two given points into y = ax. b. b. 2 = a 3. b. 9 = a 6. EXAMPLE 4. Write a power function. SOLUTION. STEP 1. Substitute 2 for y and 3 for x.

krobbie
Télécharger la présentation

EXAMPLE 4

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. b Write a power function y = axwhose graph passes through (3, 2) and (6, 9) . Substitute the coordinates of the two given points into y = ax. b b 2 = a 3 b 9 = a 6 EXAMPLE 4 Write a power function SOLUTION STEP 1 Substitute 2 for yand 3 forx. Substitute 9 for yand 6 forx.

  2. Solve for ain the first equation to obtain a= , and substitute this expression for ain the second equation. Log 4.5 2 Substitute for ain second equation. b 9 = 6 b Log2 3 2 3 b Log 4.5 = b 2 b Take log of each side. 2 9 = 2 2 b 4.5 = 2 2 3 b = b 2.17 b EXAMPLE 4 Write a power function STEP 2 Simplify. Divide each side by 2. Change-of-base formula Use a calculator.

  3. 2 3 2.17 2.17 Determine that a = 0.184. So, y = 0.184x. EXAMPLE 4 Write a power function STEP 3

  4. b Write a power function y = ax whose graph passes through the given points. for Example 4 GUIDED PRACTICE 5. (2, 1), (7, 6)

  5. b Write a power function y = ax whose graph passes through the given points. Substitute the coordinates of the two given points into y = ax. b b 4 = a 3 b 15 = a 6 for Example 4 GUIDED PRACTICE 6. (3, 4), (6, 15) SOLUTION STEP 1 Substitute 4 for yand 3 forx. Substitute 15 for yand 6 forx.

  6. Solve for ain the first equation to obtain a= , and substitute this expression for ain the second equation. b 15 = 6 15 4 Substitute for ain second equation. b 3 4 b 15 = 4 2 b = 2 4 3 b Log 3.7 = b 2 Take log of each side. 4 2 3 b for Example 4 GUIDED PRACTICE STEP 2 Simplify. Divide each side by 4. 3.7 = 2

  7. 4 3 1.9 1.91 = 1.9 Determine that a = 0.492. So, y = 0.492x. 0.5682 Log 3.7 Log2 0.3010 = b 1.90 b for Example 4 GUIDED PRACTICE Change-of-base formula Simplify. Use a calculator. STEP 3

  8. b Write a power function y = ax whose graph passes through the given points. Substitute the coordinates of the two given points into y = ax. b b 8 = a 5 b 34 = a 10 for Example 4 GUIDED PRACTICE 7. (5, 8), (10, 34) SOLUTION STEP 1 Substitute 8 for yand 5 forx. Substitute 34 for yand 10 forx.

  9. Solve for ain the first equation to obtain a= , and substitute this expression for ain the second equation. b 34 = 10 17 8 Substitute for ain second equation. b 5 4 b 34 = 8 2 b = 2 8 5 b Log 4.2 = b 2 Take log of each side. 8 2 5 b for Example 4 GUIDED PRACTICE STEP 2 Simplify. 4.2 = 2

  10. = b Log 4.2 0.6284 Log2 0.3010 2.09 Determine that a =0.278. So, y = 0.278x. = b 2.09 b for Example 4 GUIDED PRACTICE Change-of-base formula Simplify. Use a calculator. STEP 3

  11. for Example 4 GUIDED PRACTICE 8.REASONINGTry using the method of Example 4 to find a power function whose graph passes through (3, 5) and (3, 7). What can you conclude? SOLUTION The points cannot form a power function.

More Related