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Rational Functions Quadratic Functions Square Root Functions Absolute Value Exponential Rational Exponents Rational Expressions

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Rational Functions Quadratic Functions Square Root Absolute Value Exponential Rational Exponents Rational Expressions

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Function Explorer

Function Type: Quadratic (a(x-h)² + k) Rational (a/(x-h) + k) Square Root (a√(x-h) + k) Absolute Value a|x-h| + k Exponential (a·b^(x-h) + k)

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Base Function Horizontal Shift Vertical Shift Stretch/Compression Reflection Final Function

📝 Step-by-Step Transformations

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Functions Practice Module

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Describe all transformations, key features, and graph behavior.

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Rational Functions- MCR3U Test1

MCR3U – Rational Functions & Expressions

Unit Test

Time: 90–100 minutes

Total Marks: 100

Name: ____________________________

Instructions

• Show all your work to receive full marks.
• Simplify all answers where possible.
• Use proper notation for rational expressions and exponents.
• Calculators may be used unless otherwise noted.

Section A: Rational Function Transformations

[10 Marks]

Describe the vertical/horizontal shifts, reflections, stretches or compressions relative to \( f(x) = \frac{1}{x} \).

1. \( g(x) = \frac{-2}{3(x-4)} + 4 \)

2. \( h(x) = \frac{3}{\frac{1}{2}(x-4)} + 2 \)

3. \( k(x) = \frac{-1}{x+5} - 3 \)

4. \( m(x) = \frac{4}{-2(x-1)} + 1 \)

5. \( p(x) = \frac{-3}{\frac{x}{2} + 1} + 5 \)