Question
A function g(x) has x-intercepts at (StartFraction 1 Over 2 EndFraction, 0) and (6, 0). Which could be g(x)?
g(x) = 2(x + 1)(x + 6)
g(x) = (x – 6)(2x – 1)
g(x) = 2(x – 2)(x – 6)
g(x) = (x + 6)(x + 2)
g(x) = 2(x + 1)(x + 6)
g(x) = (x – 6)(2x – 1)
g(x) = 2(x – 2)(x – 6)
g(x) = (x + 6)(x + 2)
Answers
Answered by
GPT 3.5
To find the function that corresponds to the x-intercepts given, we need to determine which function would result in those intercepts.
Given x-intercepts at (1/2, 0) and (6, 0), we know that the factors for g(x) must include (x - 1/2) and (x - 6).
Looking at the options provided:
1. g(x) = 2(x + 1)(x + 6) does not have (x - 1/2) as a factor.
2. g(x) = (x – 6)(2x – 1) does not have (x - 1/2) as a factor.
3. g(x) = 2(x – 2)(x – 6) has (x - 6) already but not (x - 1/2).
4. g(x) = (x + 6)(x + 2) does not have (x - 1/2) as a factor.
Therefore, the function that could correspond to the given x-intercepts is g(x) = 2(x – 2)(x – 6).
Given x-intercepts at (1/2, 0) and (6, 0), we know that the factors for g(x) must include (x - 1/2) and (x - 6).
Looking at the options provided:
1. g(x) = 2(x + 1)(x + 6) does not have (x - 1/2) as a factor.
2. g(x) = (x – 6)(2x – 1) does not have (x - 1/2) as a factor.
3. g(x) = 2(x – 2)(x – 6) has (x - 6) already but not (x - 1/2).
4. g(x) = (x + 6)(x + 2) does not have (x - 1/2) as a factor.
Therefore, the function that could correspond to the given x-intercepts is g(x) = 2(x – 2)(x – 6).
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