If you're given a function, you replace f(x) or y with 0 and solve for x.
For example, y = 5x-10 is solved like so
y = 5x-10
0 = 5x-10
-5x = -10
x = -10/(-5)
x = 2
Showing that x = 2 is the root to y = 5x-10. The term "root" is the same as a solution or a zero of a function.
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If you're given a graph, you look to where the graph crosses the x axis to find the roots. These locations are known as the x intercepts. The graph may cross the x axis or it might touch the axis and bounce back.
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If you're given a table of values, you look for when y is equal to 0 in the table. Whatever x value(s) pairs with y = 0 is your answer(s). This backs up what was mentioned at the top of this solution.