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Lesson 2-5: Polynomial Functions

Lesson 2-5: Polynomial Functions. Advanced Math Topics. Direct Variation. A direct variation function has the form f(x) = kx n k cannot = 0 and n is positive k is the constant of variation (rate of change/slope). Example 1.

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Lesson 2-5: Polynomial Functions

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  1. Lesson 2-5: Polynomial Functions Advanced Math Topics

  2. Direct Variation • A direct variation function has the form • f(x) = kxn • k cannot = 0 and n is positive • k is the constant of variation (rate of change/slope)

  3. Example 1 • The weight, w, of an adult male hognose snake varies directly with the cube of its length, l. Write a direct variation function that describes weight in terms of length if a snake that is 0.4 m long weighs 27.7 g.

  4. Example 2 • Write a direct variation equation for the direct variation function. f(3) =81 and n = 2

  5. try on your own • The weight, w, of a ball bearing made from a particular kind of steel varies directly with the cube of its radius, r. A ball bearing that has a radius of 0.4 cm has a weight of 2.1 g. Write a direct variation function that describes weight in terms of radius.

  6. Polynomial Function • The sum of one or more direct variation functions is a polynomial function. The sum may also include a constant function(# w/o variable). • Example: P(x)= x4 + 16x3 + 5x2- 13x + 6 • Degree of a Polynomial Function • Degree of a polynomial is determined by the highest exponent! • For the previous example there is a degree of 4

  7. Example 3 • Use the polynomial function P(x)=2x4 + 0.2x3 - x2 + 1 • Find P(-2) • Find P(3a)

  8. try on your own • Use the function P(x) = -3x5 + 5x2 – x + 4 • Find P(1) • Find P(-2k)

  9. Example 4 • Use the function f(x) = ½x – 4 • Is f a polynomial function? What is its degree? What other types of function is this? • Find x so that f(x) = -1

  10. Try on your own • Use the function g(x) = -x2 + 3x - 1 • Is g a polynomial function? What is its degree? What other types of function is this? • Find x so that g(x) = -1

  11. Zeros of a Function • A zero of a function is a value of x that makes f(x) equal to zero. • You can get the zeros by factoring the function then set each factor equal to zero to find the x values • If the function is already in factored form you go right to setting each term equal to 0 and solve for x

  12. The function for volume of a prism is V(x)= l x w x h use the diagram to the right to find the zeros of the function. Example 5 2x+6 2x x+8

  13. Using Zeros to Graph • 1. Find zeros • 2. Graph them on the x axis • 3. Plug in points for x that are between and beyond the zeros to see the shape of the graph. • 4. Graph them and connect with a smooth curve

  14. Example 5 Cont… • Use the zeros of the function to graph the equation of the polynomial function for the volume of a prism. f(x)=x(x+3)(x+2)

  15. Example 6 • Find the zeros of the function • Graph the function (when you are done check your graph on the calculator) f(x) = x3 – 36x

  16. Try on your own • Find the zeros and graph the function y=x3+5x2+6x

  17. Try on your own • Graph the function • f(x)= 1 (x-4)(x-3)(x+2)(x+1) 10

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