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PLEASE HELP 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)?

PLEASE HELP The graph of gx is transformed from its parent function fx Apply concepts involved in determining the key features of a rational function to determi class=

Respuesta :

altavistard
g(x) = 1 / (x+4) is a modification of the "parent function" f(x) = 1/x, whose domain is the set of all real numbers other than x = 0 (cannot divide by zero).  Similarly, the range of f(x) is "all real numbers other than y=0."

g(x) has the same graph as does f(x), with the exception that the graph of f(x) has been moved (translated) 4 units to the left.  Whereas x could not = 0 before, now x cannot equal -4, because then the denom. of g(x) would be zero.

In this transformation the range remains the same from f(x) to g(x).

  Domain of a function is defined by the x-values (Input values) and Range is defined by the y-values (output values).

Domain of the given function 'g' → (-∞, -4)∪(-4, ∞)

Range of the given function 'g' → (-∞, 0)∪(0, ∞)

  Function given in the function,

  • g(x) = [tex]\frac{1}{x+4}[/tex]

For x = -4, given function is not defined [Since, g(x) has the vertical asymptote at x = -4]

For y = 0, function 'g' is not defined [Since, g(x) has the horizontal asymptote at y = 0]

  Therefore, domain of the function will be all x- values except x = -4 Or (-∞, -4)∪(-4, ∞) and range of the function will be all y-values except y = 0 Or (-, 0)∪(0, ∞).

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