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The function f(x) is a logarithmic function that has been translated horizontally. The graph of f(x) is shown below. Enter f(x)

The Function Fx Is A Logarithmic Function That Has Been Translated Horizontally The Graph Of Fx Is Shown Below Enter Fx class=

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Answer:

[tex]f(x)=\log(x-3)[/tex]

Step-by-step explanation:

The parent logarithmic function, f(x) = log(x), has a vertical asymptote at x = 0. It begins in quadrant IV, passes through the x-axis at point (1, 0) and continues into quadrant I. The end behaviours are:

  • As x → 0⁺, f(x) → -∞.
  • As x → +∞, f(x) → +∞.

When the parent logarithmic function is translated horizontally by n units, we add n to x when the translation is to the left, and subtract n from x when the translation is to the right.

The given graphed logarithmic function crosses the x-axis at point (4, 0), which indicates that it is the parent logarithmic function translated 4 units to the right. Therefore, the equation of the graphed function is:

[tex]\Large\boxed{f(x)=\log(x-3)}[/tex]

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