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Identify the equation that translates [tex]y = \ln(x)[/tex] five units down.

A. [tex]y = \ln(x - 5)[/tex]
B. [tex]y = \ln(x) + 5[/tex]
C. [tex]y = \ln(x + 5)[/tex]
D. [tex]y = \ln(x) - 5[/tex]

Sagot :

GinnyAnswer
To solve this problem, we need to identify how to translate the equation [tex]\( y = \ln(x) \)[/tex] five units down. A downward translation of a function can generally be represented by subtracting a constant from the function's output.

Given:
[tex]\[ y = \ln(x) \][/tex]

To translate this function five units down, we subtract 5 from the output of the function, resulting in:
[tex]\[ y = \ln(x) - 5 \][/tex]

Therefore, the equation that translates [tex]\( y = \ln(x) \)[/tex] five units down is:
[tex]\[ y = \ln(x) - 5 \][/tex]

So the correct answer is:
[tex]\[ y = \ln(x) - 5 \][/tex]
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