1 Form a polynomial whose zeros and degree are given Zeros 0

1) Form a polynomial whose zeros and degree are given. Zeros: 0, -3, 4 ; Degree 3

2) For the polynomial, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x -intercept. f(x) = x/5(X² - 7)

3)Determine the maximum number of turning points of f. f(x) = (x - 3)(x + 5)²

4)Find the domain of the rational function. g(x) = x+9/x²-64

5)Give the equation of the oblique asymptote, if any, of the function. f(x) = 2x³ - 5x² + 13x + 8 / x²- 3x + 8

6) Find the vertical asymptotes of the rational function. f(x) = 2x/x - 8

list and explain steps

Solution

1) Form a polynomial whose zeros and degree are given. Zeros: 0, -3, 4 ; Degree 3

polynomial f(x)=(x-0)(x-(-3))(x-4)

f(x)=x(x+3)(x-4)

f(x)=x(x²-x-12)

f(x)=(x³-x²-12x)