Medium Level
Advanced Math
Master function transformations, radical equations, and rational expressions.
What You'll Learn
Function Transformations
Understand shifts, reflections, stretches, and compressions of functions.
Radicals
Simplify radical expressions and solve radical equations.
Rational Expressions
Add, subtract, multiply, and divide rational expressions.
Complex Numbers
Work with imaginary numbers and perform operations with complex numbers.
Key Concepts
- •Vertical Shifts: f(x) + k shifts the graph up by k units
- •Simplifying Radicals: √(ab) = √a × √b and rationalizing denominators
- •Rational Equations: Find LCD when adding or subtracting rational expressions
- •Imaginary Unit: i = √(-1) and i² = -1
- •Domain Restrictions: Identify values that make denominators zero or radicands negative
Example Problem
Simplify: √50 + √18
Solution:
√50 = √(25 × 2) = 5√2
√18 = √(9 × 2) = 3√2
√50 + √18 = 5√2 + 3√2 = 8√2
Study Tips
- ✓Graph transformations systematically: start with the parent function, then apply transformations in order
- ✓Always check for extraneous solutions when solving radical or rational equations
- ✓Factor completely before simplifying rational expressions
- ✓Remember that i² = -1, i³ = -i, and i⁴ = 1 (the pattern repeats)
Start Practicing
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