Graph Axes: How To Identify Positive And Negative Roots Of Math Functions

When the graph crosses the x-axis (positive to negative, negative to positive)

Find the maximum/minimum values of f(x) given a graph of f ‘(x).

When a graph crosses the x-axis, it means that the function being graphed has a root or a zero at that point. In other words, the value of the function at that point is equal to zero. When a graph crosses the x-axis from positive to negative, it means that the function is decreasing and changing signs at that point, indicating that the root or zero is a negative number. Similarly, when a graph crosses the x-axis from negative to positive, it means that the function is increasing and changing signs at that point, indicating that the root or zero is a positive number.

For example, consider the function f(x) = x^2 – 4. When graphed, this function is a parabola that opens upwards and has its vertex at (0,-4). The roots of this function can be found by setting f(x) equal to zero and solving for x:

x^2 – 4 = 0
x^2 = 4
x = ±2

Therefore, the function has two roots, x = -2 and x = 2, which can be seen on the graph as points where the function crosses the x-axis. Furthermore, since the function is negative to the left of x = -2 and positive to the right of x = 2, we can conclude that these roots are negative and positive, respectively.

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