The correct statement is f(x) is positive for all x > -4.
How to determine sign of function
Given function f(x) = (x - 7)/x² - 3x - 28
Let's factor the denominator of the equation.
f(x) = (x - 7)/(x - 7)(x + 4)
Cancel out the common factor (x - 7) from the numerator and denominator.
f(x) = 1/x + 4
For the denominator
x + 4 = 0
x = - 4
Observe that f(x) is positive for all x > -4 because the fraction is always positive for positive values of x.
Let test x = -3 and x = -6
For x = -3
f(x) = 1/(-3+4) = 1 (+ve)
For x = -6
f(x) = 1/(-6 +4) = -1/2 (-ve)
The function is positive for all x> -4 and negative for all x < -4
Therefore, the correct statement is f(x) is positive for all x > -4.
Complete question