An x-intercept is the point where a function crosses the x-axis on a graph. At this point, the value of y is zero, because the graph touches or crosses the horizontal axis. In coordinate terms, an x-intercept has the form (X, 0).
To find the x-intercept of a function, you set the output (y) equal to zero and solve for x. This means solving the equation:
f(x) = 0
The solution(s) will give you the x-value(s) where the function touches or crosses the x-axis. A function may have one, several, or no x-intercepts, depending on its shape and whether it crosses the x-axis at all.
For example, consider the function:
f(x) = x² – 4
To find its x-intercepts, set the function equal to zero:
x² – 4 = 0
x² = 4
x = ±2
So the graph has two x-intercepts: (–2, 0) and (2, 0). These are the points where the graph touches the x-axis, as shown below.
X-intercepts are useful for understanding the roots or zeros of a function and are often used in solving equations, graphing, and analyzing real-world scenarios where something reaches a baseline value.
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