# How do you write positive and negative intervals, increasing/decreasing intervals

I do not understand positive and negative intervals and increasing/decreasing intervals. I included 2 examples from my textbook which I did not understand and I was wondering if someone can explain it to me.

Example 1:

f(x) = 2 - x

x intercept is (2, 0) and y-intercept is (0,2)

f(x) is positive when xε(-∞, 2) and negative xε(2, ∞)
f(x) is decreasing when xε(-∞, ∞)

reciprocal od the function is g(x) = 1 / 2 - x

reciprocal function is positive when xε(-∞, 2) and negative xε(2, ∞)
It is increasing when xε(-∞, 2) and when xε(2, ∞)

Example 2:

f(x) = 9 - x^2

x-intercepts are 3 and -3

f(x) is positive when xε(-3, 3) and negative when xε(-∞, -3) and when xε(3, ∞)
f (x) is increasing when xε(-∞, 0) and decreasing when xε(0, ∞)

g(x) = 1 / 9- x^2

reciprocal function is positive when xε(-3, 3) and negative xε(-∞, -3) and when xε(3, ∞)
It is decreasing when xε(-∞, -3) and when xε( -3, 0) and increasing when xε(0, 3) and when xε(3, ∞)

eumyang
Homework Helper
Example 1:

f(x) = 2 - x

x intercept is (2, 0) and y-intercept is (0,2)

f(x) is positive when xε(-∞, 2) and negative xε(2, ∞)
xε(-∞, 2) means x < 2. When x < 2, f(x) > 0.
xε(2, ∞) means x > 2. When x >2, f(x) < 0.
f(x) is decreasing when xε(-∞, ∞)
When you look at the graph from left to right, the x values are increasing. As the x values increase, the corresponding f(x) values are decreasing.

Example 2:

f(x) = 9 - x^2

x-intercepts are 3 and -3

f(x) is positive when xε(-3, 3) and negative when xε(-∞, -3) and when xε(3, ∞)
f (x) is increasing when xε(-∞, 0) and decreasing when xε(0, ∞)
xε(-∞, 0): for all values "between" -∞ and 0 (ie. the left side of the graph), as you look left to right, the corresponding f(x) values are increasing.
xε(0, ∞): for all values "between" 0 and ∞ (ie. the right side of the graph), as you look left to right, the corresponding f(x) values are decreasing.