In 31-40, for each polynomial function f(x): a) State the degree of the function
ID: 3115379 • Letter: I
Question
In 31-40, for each polynomial function f(x): a) State the degree of the function and then describe the end behavior of f(x). b) Find the zeros of f(x) and determine if the graph crosses or touches the x-axis at each intercept. Determine the y-intercept. Sketch the graph of f(x). Determine the number of turning points f(x) has. nes 37' 3 c) d) e) 32. f(x)--x' + 16x' 34. f(x)--2x2(x-1)2(x + 5) 36, f(x) = (x + 3)(x + 1 )3(x + 4) 38. f(x)-4x3 40, f(x) =-(x-3)2(x + 2) f(x) = x2(x-1),(x + 2) 35) f(x) = (x + 2)2(x-1 )3(x + 3) f(x) =-r-2z? f(x) = (x-4)(x + 1)(x-2)Explanation / Answer
Here I'm giving you a simple formula to find number of turning points of given function : number of zeros-1 +number of even zero's.
35)f(x)=(x+3)^2+(x-1)^3+(x+3)
Number of turning points is equal to = 3-1+1=3.
39)f(x)=(x-4)(x+1)(x-2)
Number of turning points= 3-1+0=2.
33)f(x)=x^2(x-1)^3(x+2)
Number of turning points= 3-1+1=3.
31)f(x)=x^4-9x^2
Number of turning points=2-1+2=3.
37) f(x)=-x^3-2x^2
Number of turning points =2-1+1 =2.
In this way we can determine turning points for a given polynomial.
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