# What is the range of y=ln(x-1)+6

baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

What is the range of `y=ln(x - 1)+6?`

The graph of y = ln(x).

The range is all real numbers as the graph continues to decrease as x approaches zero, and the graph continues to increase as x increases.

The graph of y = ln(x-1) + 6 is shifted to the right 1 and up 6 units from y = ln(x).

Therefore, the range is all real numbers.

Range:  `(-oo,oo)`

``

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

The range of a function f(x) is all the values that f(x) can take when x lies in the domain of the function.

The logarithm ln(x) of any real number x is defined if x lies in the set `(0, oo)` . The logarithm can also take on any value from `-oo` to `oo` based on what the value of x is.

The domain of the function f(x) = ln(x - 1) + 6 is `(1, oo)` .

For x lying in `(1, oo)` , f(x) = ln(x - 1) + 6 can take on all real values lying in `(-oo, oo)` . This is the range of the function.