f(x) = 1 - ln (x-2) a.  What is the domain of f? , b.  what is the range of f?, c. what are the x-intercepts of the graph of f?,  

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embizze | High School Teacher | (Level 1) Educator Emeritus

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Given `f(x)=1-ln(x-2)` :

(a) The base function is `lnx` . This function has been reflected across the x-axis (the negative coefficient), translated 2 units to the right and one unit up.

(b) The domain of `lnx` is `x>0` or `(0,oo)` . Reflecting the graph and translating up did not change the domain, but translating to the right changed the domain to x>2 or `(2,oo)`

(c) The range of `lnx` is all real numbers, and the range of the transformed function is still all real numbers.

(d) The x-intercept of `lnx` is 1. Reflecting across the x-axis does not change the x-intercept. But the horizontal and vertical translations do change the intercept.

`0=1-ln(x-2)`

`ln(x-2)=1`

`e^(ln(x-2))=e^1`

`x-2=e==>x=e+2~~4.718281828`

The graph:

Sources:

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