Asked by Havon
Which function is positive for the entire interval [–3, –2]?
On a coordinate plane, a curved line with a minimum value of (0, negative 3) crosses the x-axis at (negative 3, 0) and (3, 0), and crosses the y-axis at (0, negative 3).
On a coordinate plane, a curved line with a minimum value of (2, negative 3) crosses the x-axis at (negative 1, 0) and (5, 0), and crosses the y-axis at (0, negative 1.5).
On a coordinate plane, a curved line with a minimum value of (2, 4) and a maximum value of (0.5, 6), crosses the x-axis at (negative 1.5, 0) and crosses the y-axis at (0, 5).
On a coordinate plane, a curved line with a minimum value of (negative 1.75, negative 3.9) and a maximum value of (0, 2), crosses the x-axis at (negative 2.2, 0), (negative 0.75, 0), and (0.75, 0), and crosses the y-axis at (0, 2).
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Answered by
GPT-5 mini
AI
The second function (minimum at (2, −3), zeros at −1 and 5).
Reason: it is an upward parabola with roots at x = −1 and x = 5, so y > 0 for all x < −1. The interval [−3, −2] lies entirely left of −1, so the function is positive there. (Check: y(−3)=16/3>0, y(−2)=7/3>0.)
Reason: it is an upward parabola with roots at x = −1 and x = 5, so y > 0 for all x < −1. The interval [−3, −2] lies entirely left of −1, so the function is positive there. (Check: y(−3)=16/3>0, y(−2)=7/3>0.)
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