# Math Help - Finding range of piecewise function

1. ## Finding range of piecewise function

The function is (1)/((3^(x^2+1)) for x is greater than or equal to zero and

5x + 3 for x is less than 0.

I understand the range of 5x + 3 under these circumstances is y
is less than or equal to 3 (and this is also the range for the entire piecewise function). I don't understand how to find the range of the first part of the piecewise function with teh fractional exponent. My book doesn't explain it well.

2. ## Re: Finding range of piecewise function

Originally Posted by benny92000
The function is (1)/((3^(x^2+1)) for x is greater than or equal to zero and

5x + 3 for x is less than 0.

I understand the range of 5x + 3 under these circumstances is y
is less than or equal to 3 (and this is also the range for the entire piecewise function). I don't understand how to find the range of the first part of the piecewise function with teh fractional exponent. My book doesn't explain it well.
note $f(0) = \frac{1}{3}$

what happens to $\frac{1}{3^{x^2+1}}$ for $x > 0$ ?

1/3>y>0

4. ## Re: Finding range of piecewise function

Originally Posted by benny92000
1/3>y>0
ok ... so, what's the range of f(x)?