Problem preview

F-BF.3 Warmup M3-019-A07-V02

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

Analyze a transformed logarithm and its domain boundary

Problem

Analyze \(y~=~-\log_{2}(x~+~4)\) relative to \(y~=~\log_{2}(x)\). State the base and transformations, vertical asymptote, domain, and image of parent point \((1,~0)\).

Answer choices

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Base: 2. Transformations: left 4, x-axis reflection. Asymptote: x=-3. Domain: (-3,∞). Point: (1,0)→(-4,0).

Base: 2. Transformations: right 4, x-axis reflection. Asymptote: x=4. Domain: (4,∞). Point: (1,0)→(5,0).

Base: 2. Transformations: left 4, x-axis reflection. Asymptote: x=-4. Domain: (-∞,-4). Point: (1,0)→(-3,0).

Base: 2. Transformations: left 4, x-axis reflection. Asymptote: x=-4. Domain: (-4,∞). Point: (1,0)→(-3,0).

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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: Analyze a transformed logarithm and its domain boundary