What are the domain and range of f(x) = 1/6x +2

Hello from MrBillDoesMath!

My interpretation of f(x) is f(x) = (1/6x) + 2

Domain =  {Real Numbers} - {0}

Range = {Real Numbers}

Discussion:

Domain of f = all x where f(x) is defined. For f(x) the only singularity occurs at x = 0 so the domain is the set of all real numbers except for 0. For x>0, x values close to 0 cause y to grow large while large x causes y to approach 0.  A similar argument for x <0 shows that the range of f is all real numbers.

Thank you,

MrB

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answer

d. 10

explanation

the distance from point y to wx is the height of the triangle.

using pythagoras theorem,

group similar terms to get,

this implies that,

take positive square root of both sides to get,

this implies that,