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## 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?

• 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.
• 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)?
• @celestec1, I do not think there is a y-intercept because the line is a function. This is just based on my opinion
• So zero is not a positive number?
• Correct. Zero is the dividing point between positive and negative numbers but it is neither positive or negative.
• I have a question, what if the parabola is above the x intercept, and doesn't touch it? Is there not a negative interval?
• Correct. For example, the graph of x^2 + 5 is always positive and never crosses the x-axis. To prove this, put x=0 in the equation. 0 squared is obviously 0, then you are left with positive 5. That is the "lowest" the curve ever gets.
• This linear function is discrete, correct?
• No, this function is neither linear nor discrete. It is continuous and, if I had to guess, I'd say cubic instead of linear.
• 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.
• I'm not sure what you mean by "you multiplied 0 in the x's". If you mean that you let x=0, then f(0) = 0^2-4*0 then this does equal 0. So, f(0)=0. This function decreases over an interval and increases over different intervals.
• 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.