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The table represents a logarithmic function f(x).

x y
1 over 125 −3
1 over 25 −2
one fifth −1
1 0
5 1
25 2
125 3

Use the description and table to graph the function, and determine the domain and range of f(x). Represent the domain and range with inequality notation, interval notation, or set-builder notation. Explain your reasoning.



Answer :

The domain and range of the logarithmic equation is represented in interval notation as

  • Domain: (0, ∞)
  • Range: (-∞, ∞)

How to determine the domain and range of f(x)

The function in the table is a logarithm function in base 5, which is equal to

㏒₅(1/125) = -3

㏒₅(1/25) = -2

㏒₅(1/5) = -1

hence the function is written as

y = ㏒₅x

The domain of logarithmic functions is positive real numbers while the range is set of real numbers

The plotted graph shows that the domain is always approaching 0 but never zero hence it all positive real numbers.

The range is viewing from the graph, the values is form positive to negative and hence all real numbers

the domain in inequality notation is written as: 0 < x < ∞

the range written in inequality notation is: -∞ < y < ∞

Learn more about range and domain at:

https://brainly.com/question/2264373
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