# Math Help - Confusing SAT Study Question

1. ## Confusing SAT Study Question

Here is the link to the problem but I don't understand the given explanation.

https://quickstart.collegeboard.com/...th_popup1.html

2. I think the first thing you have to know that y = f(x). So for the given ordered pairs: (a, b) in the diagram, x = a and y = f(x) = b.

From the graph of f, you can see that for any value of x strictly between 1 and 4, the value of f(x) is greater than 0.

You can see from the diagram that the line of the graph is above the x-axis, and therefore positive, when x is between (1,0) and (4,0).

For any value of x greater than 8 and less than or equal to 10, the value of f(x) is greater than 0.

You can also see the same from the diagram that the line of the graph is positive, when x is between (8,0) and (10,t). Here it doesn't matter what t is, all you need to know is that the line of the graph is above the x-axis.

For any other value of x between -2 and 10 inclusive, the value of f(x) is less than or equal to 0.

All other values of x not included in the above stated intervals, (between (1,0) & (4,0) and (8,0) & (10, t)), the graph is negative, as you can see in the diagram because the line of the graph is below the x-axis.

So the values of x for which f(x) is positive are those for which 1 < x < 4 or 8 < x 10.

Taking the text that I used to explain earlier, translate it into the language of math:

1. x is positive between (1,0) & (4,0): 1 < x < 4
2. x is positive between (8,0) & (10, t): 8 < x $\leq$ 10

*note: the difference between $<$ and $\leq$ is that the point (10,t) is not on the x-axis, so the point itself is included. (i.e. y = f(x) = f(10) = t)