Substitute the coordinates of the two given points into y = ax .

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Presentation transcript:

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

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

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

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

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

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

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

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

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

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

GUIDED PRACTICE for Example 4 8. REASONING Try 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.