Question

Sketch the graph of the function. $$ y=\ln (x-1) $$

   Sketch the graph of the function.
$$
y=\ln (x-1)
$$

Calculus an Applied Approach

Calculus an Applied Approach

Ron Larson, David C,… 8th Edition

Chapter 4, Problem 13

Instant Answer

Solved by Expert Kevin W.

06/30/2021

Step 1

The graph of $y=\ln(x)$ is a curve that starts from negative infinity at $x=0$ and increases slowly as $x$ increases. The graph is undefined for $x\leq 0$. Show more…

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Sketch the graph of the function. $$ y=\ln (x-1) $$

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Key Concepts

Natural Logarithm Function

The natural logarithm function, denoted as ln(x), is the inverse of the natural exponential function e^x. It is defined for positive values of x and is known for its slow growth rate as x increases. The function has a vertical asymptote at x = 0, meaning it approaches negative infinity as x approaches zero from the right. Its graph passes through the point (1, 0) because ln(1) = 0.

Horizontal Transformation

A horizontal transformation involves shifting the graph of a function left or right. In the function y = ln(x - 1), the subtraction inside the logarithm indicates a horizontal shift. Specifically, the graph of ln(x) is shifted to the right by 1 unit, changing the original domain from x > 0 to x > 1 and moving the vertical asymptote from x = 0 to x = 1.

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