About this video
In this short worked example the narrator highlights intervals on a graph where f(x) < 0 (where the graph is below the x-axis) and where f(x) > 0 (where it is above the x-axis). Any such region works as an answer.
You'll be able to
- find an interval where a function is negative by looking below the x-axis.
- find an interval where a function is positive by looking above the x-axis.
Key words
- f(x) < 0
- The function's value is negative, so the graph is below the x-axis.
- f(x) > 0
- The function's value is positive, so the graph is above the x-axis.
Transcript
A function, f of x, is plotted below. Highlight an interval where f of x is less than 0. So f of x-- which is really being plotted on the vertical axis right over here-- x is the horizontal axis. f of x being less than 0 really means that the graph is below the x-axis.
So the function is negative in this interval right over here and this interval over here. So I could put this anywhere right over here, or I could stick it anywhere right over here. Let me stick it right over here. There we go. Got it right. Let's do a couple more.
So the function is plotted below. Highlight an interval where f of x is greater than 0. So I could do this area right over here where the function is above the x-axis, or I could do this area right over here where the function goes way above the x-axis. Well, it even goes off the page.
So let's stick it right over here. Let's do one more. So highlight an interval where f of x is greater than 0. Once again, I can do this region right over here where the function is above the x-axis, or over here where it's above the x-axis. I'll do it here just for fun.
There we go.
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