To determine the sign of the function f(x) = x^2 + 2x - 15, we need to find the intervals where the function is positive or negative.
First, let's factor the function: f(x) = (x - 3)(x + 5)
The function is positive when both factors have the same sign (positive), and negative when the factors have different signs (one is positive and the other is negative).
Looking at the factors individually:
(x - 3) is positive when x > 3 and negative when x < 3.
(x + 5) is positive when x > -5 and negative when x < -5.
To determine the sign of the function for different intervals, we can create a sign chart:
-∞ -5 3 +∞
---------------------------------------------------------
(x - 3) | - - + +
(x + 5) | - + + +
From the sign chart, we see that:
- For x < -5, both factors are negative, so f(x) is positive.
- For -5 < x < 3, (x - 3) is negative and (x + 5) is positive, so f(x) is negative.
- For x > 3, both factors are positive, so f(x) is positive.
Therefore, the sign of the function f(x) = x^2 + 2x - 15 is positive for x < -5 and x > 3, and negative for -5 < x < 3.
determine the sign of the function f(x) = x^2+2x-15
1 answer