Problem preview

F-BF.3 Warmup M3-019-A05-V02

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

Analyze a transformed reciprocal parent and its asymptotes

Problem

Analyze \(y~=~-2/(x~+~4)\) relative to \(y~=~1/x\). State the parent, transformations, asymptotes, and domain and range exclusions.

Answer choices

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Parent: 1/x. Transformations: left 4, vertical stretch 2, x-axis reflection. Asymptotes: x=-4, y=0. Exclusions: x≠-4, y≠0.

Parent: 1/x. Transformations: left 4, vertical stretch 2, x-axis reflection. Asymptotes: x=0, y=-4. Exclusions: x≠0, y≠-4.

Parent: 1/x. Transformations: right 4, vertical stretch 2, x-axis reflection. Asymptotes: x=4, y=0. Exclusions: x≠4, y≠0.

Parent: 1/x. Transformations: left 4, vertical stretch 2, no reflection. Asymptotes: x=-4, y=0. Exclusions: x≠-4, y≠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 reciprocal parent and its asymptotes