Final answer:
The domain of g(x) = 1/(x-6) is all real numbers except x=6, and the range is all real numbers except y=0.
Step-by-step explanation:
The student has provided the function g(x) = ¹/(x-6), which is a rational function derived from a parent function f(x). To find the domain and range of g(x), we need to consider the properties of rational functions.
A. The domain of a function is the set of all possible input values (x-values) for which the function is defined. For the function g(x) = ¹/(x-6), the denominator cannot be zero since division by zero is undefined. Therefore, the domain is all real numbers except x=6, which can be written as (-∞, 6) ∪ (6, +∞).
B. The range of a function is the set of all possible output values (y-values). For g(x), as x approaches 6 from either side, g(x) grows without bound, so it can take on any real number value except for 0 (as the function never equals zero). Hence, the range of g(x) is all real numbers except 0, or (-∞, 0) ∪ (0, +∞).
Complete Question:
The graph of g(x) is transformed from its parent function, f(x). Apply concepts involved in determining the key features of a rational function to determine the domain and range of the function,
A. What is the domain of the function, g(x)?
B. What is the range of the function, g(x)?
g(x) = 1/(x-6)