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Common Mistakes

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Pre-calculus · AP · Polynomial and Rational Functions

Focus

Rates of Change in Linear and Quadratic Functions

This topic is assessed on the AP Exam.

Frequent mistakes

### 1. Hole vs asymptote confusion

What it looks/sounds like: A canceled factor is labeled as a vertical asymptote.

Why it happens: Any undefined x-value is treated the same.

How to fix: Factor fully; if cancellation occurs, describe a hole at that x-value.

### 2. Wrong end behavior

What it looks/sounds like: Leading-term signs are misread for far-left/far-right behavior.

Why it happens: Only a calculator window is used.

How to fix: Compare degrees and leading coefficients before graphing.

### 3. Correct work, wrong question

What it looks/sounds like: The algebra is fine but answers a different quantity than the stem asks for.

Why it happens: Attention locks onto the first operation instead of the final ask.

How to fix: Underline the final question; after solving, verify the boxed answer matches it.

### 4. Notation and justification gaps

What it looks/sounds like: Missing units, limit language, or ‘because’ statements AP graders expect.

Why it happens: Notation is treated as decoration rather than part of the score.

How to fix: Add one justification phrase per major step (definition, theorem, or rule).

How to avoid them

1. State domain restrictions before simplifying rationals. 2. Distinguish zeros, holes, and asymptotes on one example. 3. Predict end behavior algebraically, then check with technology.

Quick self-check

[ ] Can name one mistake specific to 1.3
[ ] Can explain how to catch it before submitting
[ ] Can redo one item with full justification

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