SOLUTION: Let f(x)=-8+3^(x+7).Find the domain and range of f(x). D:__________ R:__________

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Let f(x)=-8+3^(x+7).Find the domain and range of f(x). D:__________ R:__________      Log On


   

Question 373241: Let f(x)=-8+3^(x+7).Find the domain and range of f(x).
D:__________
R:__________
Found 2 solutions by jsmallt9, robertb:
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
The domain is the set of all possible x values. In your function. the x is in an exponent. Exponents can be any number so x can be any number. The domain is all Real numbers.

The range is the set of all possible y (or function) values. Your function value is 8 plus a power of 3. Powers of 3 can be any positive number. A power of 3 cannot be zero or negative (even with a zero or negative exponent)! In other words, powers of 3 must be greater than zero. And if the power of 3 is greater than zero, then 8 plus a power of 3 must be greater than 8. The range is all Real numbers that are greater than 8.

Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Domain is the set of all real numbers (No restrictions on the values of x!). For the range, the original equation y+=+-8+%2B+3%5E%28x%2B7%29is equivalent to log%28%28y%2B8%29%29+=+%28log3%29%2A%28x%2B7%29. Hence y +8 >0, or y > -8.