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The graph of y = f(x) is shown below. Find all values of x where f(x) = 0

The graph of y = f(x) is shown below. Find all values of x where f(x) = 0-example-1
User Sarie
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2 Answers

6 votes

The values of x where f(x) = 0 are the solutions to the equation f(x) = 0. Graphically, these are the points where the graph of f(x) intersects the x-axis. From the image, we can see that there are two such points: (2,0) and (8,0). The values of x where f(x) = 0 are x = 2 and x = 8.

In the context of a mathematical function f(x), the values of x for which f(x) = 0 are known as the roots or solutions of the equation. Graphically, these solutions correspond to the points where the graph of the function intersects the x-axis.

Observing the provided image, it is evident that the graph of f(x) intersects the x-axis at two distinct points: (2,0) and (8,0). These points represent the values of x at which f(x) equals zero.

Algebraically, these points can be confirmed by setting f(x) equal to zero and solving for x. Therefore, the solutions to the equation f(x) = 0 are x = 2 and x = 8. These values signify the x-coordinates of the points where the graph of f(x) crosses the x-axis, indicating the instances when the function output is zero.

User Mario Araque
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the graph crosses the x-axis at 2 and 8.
f(2) = 0
f(8) = 0
User Rhs
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