I NEED HELP PLEASE, THANKS! :) Determine the zeros for and the end behavior of f(x) = x(x – 4)(x + 2)^4.
1 answer:
Answer: a) zeros: x = {0, 4, -2}
b) as x → ∞, y → ∞
as x → -∞, y → ∞
<u>Step-by-step explanation:</u>
I think you mean (a) find the zeros and (b) describe the end behavior
(a) Find the zeros by setting each factor equal to zero and solving for x:
x (x - 4) (x + 2)⁴ = 0
- x = 0 Multiplicity of 1 --> odd multiplicity so it crosses the x-axis
- x = 4 Multiplicity of 1 --> odd multiplicity so it crosses the x-axis
- x = -2 <u>Multiplicity of 4 </u> --> even multiplicity so it touches the x-axis
Degree = 6
(b) End behavior is determined by the following two criteria:
- Sign of Leading Coefficient (Right side): Positive is ↑, Negative is ↓
- Degree (Left side): Even is same direction as right side, Odd is opposite direction of right side
Sign of the leading coefficient is Positive so right side goes UP
as x → ∞, y → ∞
Degree of 6 is Even so Left side is the same direction as right (UP)
as x → -∞, y → ∞
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Step-by-step explanation:
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About 750 different permutations
For #1 the answers are
69 degrees
155 degrees
86 degrees
335 degrees
249 degrees
sub x=1 into f(x),
remainder= 1^3+2(1)^2-5(1)-6= -8
since remainder≠0, x=1 is not a root of the function
sub x=-1,
remainder = (-1)^3+2(-1)^2-5(-1)-6= 0
by remainder theorem,
x=-1 is a root of f(x)
hence, the correct ans is c