Question

Find the range:

a) f(x) = ln(x+6)

b) f(x) = 2/(3x-1)

Please show steps so I can learn, I have the answers already. Thanks in advance

Answer 1

A) the range is all real numbers. If you understand how the ln graph works. For values 0-1, the range is negative. And for values above 1 are all positive and they increase/decrease exponentially.

B) The range is all real numbers except for value 0. Seeing that there is (3x-1) in the denominator, this shows that there is a vertical asymptote, the lines will stretch to infinity for y-values. This range is all real numbers. Why except 0? because there is a horizontal asymptote of y=0. since 2/(3x-1) cannot be 0.
For the denominator cannot be 0, or else it will be undefined. and since 2 not equals to 0, 2/(3x-1) cannot be equal to 0.

Answer 2

Great, thanks for your help, I appreciate it.