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Power Functions and Radical Equations

Power Functions and Radical Equations. Lesson 4.7. Properties of Exponents. Given m and m positive integers r, b and p real numbers. Power Function. Definition Where k and p are constants Power functions are seen when dealing with areas and volumes

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Power Functions and Radical Equations

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  1. Power Functions and Radical Equations Lesson 4.7

  2. Properties of Exponents • Given • m and m positive integers • r, b and p real numbers

  3. Power Function • Definition • Where k and pare constants • Power functions are seen when dealing with areas and volumes • Power functions also show up in gravitation (falling bodies)

  4. Special Power Functions • Parabola y = x2 • Cubic function y = x3 • Hyperbola y = x-1

  5. Special Power Functions • y = x-2 Text calls them "root" functions

  6. Special Power Functions • Most power functions are similar to one of these six • xp with even powers of p are similar to x2 • xp with negative odd powers of p are similar to x -1 • xp with negative even powers of p are similar to x -2 • Which of the functions have symmetry? • What kind of symmetry?

  7. Variations for Different Powers of p • For large x, large powers of x dominate x5 x4 x3 x2 x

  8. Variations for Different Powers of p • For 0 < x < 1, small powers of x dominate x x4 x5 x2 x3

  9. Variations for Different Powers of p • Note asymptotic behavior of y = x -3 is more extreme 0.5 20 10 0.5 y = x -3 approaches x-axis more rapidly y = x -3 climbs faster near the y-axis

  10. Think About It… • Given y = x –p for p a positive integer • What is the domain/range of the function? • Does it make a difference if p is odd or even? • What symmetries are exhibited? • What happens when x approaches 0 • What happens for large positive/negative values of x?

  11. Assignment • Lesson 4.7 • Page 321 • Exercises 1 – 67 EOO

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