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## Algebra 1

### Course: Algebra 1>Unit 8

Lesson 9: Intervals where a function is positive, negative, increasing, or decreasing

# Increasing, decreasing, positive or negative intervals

Function values can be positive or negative, and they can increase or decrease as the input increases. Here we introduce these basic properties of functions.

## Want to join the conversation?

• I have a question, what if the parabola is above the x intercept, and doesn't touch it? Is there not a negative interval? •  That is true, if the parabola is upward-facing and the vertex is above the x-axis, there would not be an interval where the function is negative. You have to be careful about the wording of the question though. The `function` would be positive, but the function would be decreasing until it hits its vertex or minimum point if the parabola is upward facing. If the function is decreasing, it has a negative rate of growth. In other words, while the function is decreasing, its slope would be negative. You could name an interval where the function is positive and the slope is negative. The secret is paying attention to the exact words in the question.
• does 0 count as positive or negative? •   That's a good question! Some people might think 0 is negative because it is less than 1, and some other people might think it's positive because it is more than -1. But in actuality, positive and negative numbers are defined the way they are BECAUSE of zero. If a number is less than zero, it will be a negative number, and if a number is larger than zero, it will be a positive number. So zero is actually neither positive or negative.
Zero can, however, be described as parts of both positive and negative numbers. For example, if someone were to ask you what all the non-negative numbers were, you'd start with zero, and keep going from 1 to infinity. (0, 1, 2, 3, 4...to infinity) Alternatively, if someone asked you what all the non-positive numbers were, you'd start at zero and keep going from -1 to negative-infinity. (0, -1, -2, -3, -4 ... to -infinity)
BUT what if someone were to ask you what all the non-negative and non-positive numbers were? Well, then the only number that falls into that category is zero!
• At the sign is little bit confusing. More explanation. Thanks • Sal wrote b < x < c. Between the points b and c on the x-axis, but not including those points, the function is negative. Notice, as Sal mentions, that this portion of the graph is below the x-axis. That is your first clue that the function is negative at that spot. Hope this helps.
• Wouldn't point a - the y line be negative because in the x term it is negative? • No, the question is whether the `function` f(x) is positive or negative for this part of the video. That means, according to the vertical axis, or "y" axis, is the value of f(a) positive --is f(x) positive at the point a? In other words, what counts is whether y itself is positive or negative (or zero).

At point a, the function f(x) is equal to zero, which is neither positive nor negative. It makes no difference whether the x value is positive or negative.
• So zero is not a positive number? • If a function is increasing on the whole real line then is it an acceptable answer to say that the function is increasing on (-infinity, 0) and (0, infinity)? • This linear function is discrete, correct? • f(x)= x^2-4x
I multiplied 0 in the x's and it resulted to f(x)=0? Is this right and is it increasing or decreasing... I'm slow in math so don't laugh at my question. • f(x)= x^2-4x
I multiplied 0 in the x's and it resulted to f(x)=0? Is this right and is it increasing or decreasing... I'm slow in math so don't laugh at my question. • If you have a x^2 term, you need to realize it is a quadratic function. There is no meaning to increasing and decreasing because it is a parabola (sort of a U shape) unless you are talking about one side or the other of the vertex. Increasing and decreasing sort of implies a linear equation.
If it is linear, try several points such as 1 or 2 to get a trend. 