Problem preview

F-BF.3 Warmup M3-019-A03-V03

Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.

Select reflection axes and simplify the transformed function

Problem

Analyze the transformation from \(f(x)~=~\ln(x)\) to \(-\ln(-x)\). State the inside and outside effects, the resulting expression, its domain, and its vertical asymptote.

Answer choices

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Preview only

Inside effect: none. Outside effect: x-axis reflection. Result: -ln(x). Domain: (0,∞), with asymptote x=0.

Inside effect: y-axis reflection. Outside effect: none. Result: ln(-x). Domain: (-∞,0), with asymptote x=0.

Inside effect: y-axis reflection. Outside effect: x-axis reflection. Result: -ln(-x). Domain: (-∞,0), with asymptote x=0.

Inside effect: none. Outside effect: none. Result: ln(x). Domain: (0,∞), with asymptote x=0.

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Curriculum context

Course: Math III
Standard: F-BF.3
Category: Functions
Domain: Building Functions
Objective: Analyze graph transformations across radical, rational, exponential, logarithmic, and other functions; recognize even and odd functions.
Problem type: Select reflection axes and simplify the transformed function