1. 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.

2. 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 = 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 = b 2
Take log of each side. 2
Log 4.5
Log2
= b
Change-of-base formula b
Use a calculator.

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

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

5. 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.

6. 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 =
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 = b 2
Take log of each side. 2

7. 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. b
Use a calculator.
STEP 3
Determine that a = So, y = 0.492x
1.9 3 4
1.91

8. 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.

9. 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 = 8 5 b
34 = 8 2 b
Simplify.
= 2 b 17 4
4.2 = 2
Log = b 2
Take log of each side. 2

10. 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. b
Use a calculator.
STEP 3
Determine that a = So, y = 0.278x .
2.09

11. 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.