The graph of y=-1/2x+2 is positive over the interval negative infinity and 4 and negative over the interval 4 and infinity. What happens on the graph when ? Explain.

The information that we have is:

"The graph of y=-1/2x+2 is positive over the interval negative infinity and 4 and negative over the interval 4 and infinity."

Now, i guess that the question is:

"What happens on the graph when x = 4 ?"

Well, if for values of x smaller than 4 the graph is negative and for values of x larger than 4 the graph is positive, this must that the graph must cross the x-axis at some point, then with only that information, we can conclude that the graph is equal to zero when x = 4.

But we could also test it with the equation:

y = -(1/2)*x + 2

if we replace the x by a 4.

y = -(1/2)*4 + 2 = -2 + 2 = 0.

Then our previous hypothesis was correct.

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