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The functions f(x) and g(x) are shown on the graph. The image shows two graphs. The first is f of x equals log base 5 of x and it is increasing from negative infinity in quadrant four as it goes along the y-axis and passes through 0 comma 1 to turn and increase to the right to positive infinity. The second is g of x and it is increasing from negative infinity in quadrant four as it goes along x equals 3 and passes through 0 comma 4 to turn and increase to the right to positive infinity. Using f(x), what is the equation that represents g(x)? g(x) = log5(x) – 3 g(x) = log5(x) + 3 g(x) = log5(x – 3) g(x) = log5(x + 3)

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semsee45

Answer:

[tex]\text{g}(x)=\log_5(x-3)[/tex]

Step-by-step explanation:

Parent function:

[tex]\text{f}(x)=\log_5(x)[/tex]

Asymptote: a line that the curve gets infinitely close to, but never touches.

Properties of the parent function:

Vertical asymptote at x = 0.

x-intercept at (1, 0).

End behaviors:

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

Properties of the transformed function:

Vertical asymptote at x = 3.

x-intercept at (4, 0).

End behaviors:

  • As x → 3⁺, f(x) → -∞
  • As x → ∞, f(x) → ∞

Therefore, function g(x) is a translation of function f(x) by 3 units right.

Translations

[tex]\text{f}(x+a) \implies \text{f}(x) \: \textsf{translated}\:a\:\textsf{units left}[/tex]

[tex]\text{f}(x-a) \implies \text{f}(x) \: \textsf{translated}\:a\:\textsf{units right}[/tex]

[tex]\text{f}(x)+a \implies \text{f}(x) \: \textsf{translated}\:a\:\textsf{units up}[/tex]

[tex]\text{f}(x)-a \implies \text{f}(x) \: \textsf{translated}\:a\:\textsf{units down}[/tex]

Therefore,

[tex]\begin{aligned} \implies \text{g}(x) & =\text{f}(x-3)\\& =\log_5(x-3)\end{aligned}[/tex]

Learn more about graph transformations here:

https://brainly.com/question/27851068

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