Problem preview

A-SSE.1.a Warmup M3-014-A07-V02

Interpret terms, factors, and coefficients in polynomial and rational expressions.

Audit numerator zeros for rational x-intercepts or holes

Problem

For \(f(x)~=~(x~-~1)/(x~-~1)\), audit the numerator zero against the denominator. State the exclusion, cancellation, simplified value, and resulting \(x\text{-}\text{intercept}\) or hole.

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Candidate x=1: denominator 0, excluded, cancellation occurs, no x-intercept, hole (1,1). Simplified value: 1. Exclusion: x=1.

Candidate x=1: denominator 0 but allowed after cancellation, no x-intercept, no hole. Simplified value: 1. Exclusion: none.

Candidate x=1: denominator 0 but allowed, no cancellation, x-intercept (1,0), no hole. Simplified value: 1. Exclusion: none.

Candidate x=1: denominator 1, excluded, cancellation occurs, no x-intercept, hole (1,1). Simplified value: 1. Exclusion: x=1.

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Curriculum context

Course: Math III
Standard: A-SSE.1.a
Category: Algebra
Domain: Seeing Structure in Expressions
Objective: Interpret terms, factors, and coefficients in polynomial and rational expressions.
Problem type: Audit numerator zeros for rational x-intercepts or holes