SOLUTION: Suppose f(x) = (x-7)(x+4).
(a) For which values of x is the function f(x) positive? Enter your answer using inequalities.
help (inequalities)
(a) For which values of x i
Question 923836: Suppose f(x) = (x-7)(x+4).
(a) For which values of x is the function f(x) positive? Enter your answer using inequalities.
help (inequalities)
(a) For which values of x is the function f(x) negative? Enter your answer using inequalities.
help (inequalities) Found 3 solutions by ewatrrr, rothauserc, josmiceli:Answer by ewatrrr(24785) (Show Source):
You can put this solution on YOUR website! Enter your answer using inequalities
re TY
Zero is considered neither positive or negative
f(x) = (x-7)(x+4).
a) (x-7)(x+4) > 0 (Both factors >0), x > 7
0r (x-7)(x+4) > 0 (Both factors < 0) x < -4
..............
b) (x-7)(x+4)< 0
-4 < x < 7
You can put this solution on YOUR website! f(x) = (x-7)(x+4) is a parabola that crosses the x axis at (-4,0) and (7,0), the equation can be rewritten as
f(x) = x^2 -3x - 28
note that the parabola crosses the y axis at (0,-28) and it opens upward
a) x < -4 or x > 7
b) -4 < x < 7
You can put this solution on YOUR website!
For to be positive, the
factors have to be:
(+)*(+) = (+) OR
(-)*(-) = (+)
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In order for BOTH factors to be
positive,
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In order for BOTH factors to be negative,
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So, OR
Another way to say this is: is NOT allowed
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For to be negative,
factors must be:
(+)*(-) = (-) OR
(-)*(+) = (-) is REQUIRED
( just the opposite of above )
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Here's a plot of the function in order
to see this:
