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The function f(x) is represented by the equation, f(x) = x^3 – 8x^2 +x +42. Part A: Does f(x) have zeros located at 7, –2, 3? Explain without using technology and show all work. Part B: Describe the end behavior of f(x) without using technology.



Answer :

Answer:

Step-by-step explanation:

f(x) = x^3 – 8x^2 +x +42

If x = 7 is a zero then  f(7) = 0

f(7) = 7^3 - 8(7)^2 + 7 + 42

     = 343 - 392 + 49

     = 0

f(-2) and f(3) are also zero so these are also zeroes of f(x).

End behavior :

As coefficient of x^3 is positive

f(x) ascends from left from negative infinity and finally ascends to infinity on the right.

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