Function -f(x) is a reflection of f(x)
To understand the reflection of a function, we need to consider the reflection axis
To understand the reflection of a function, we need to consider the reflection axis. The reflection axis is a line that divides the graph of the function into two equal halves.
When a function is reflected over the x-axis, each point on the graph is flipped across the x-axis. This means that the y-coordinate of each point becomes its negative value. Mathematically, if (x, y) is a point on the original graph, then the corresponding point on the reflected graph is (x, -y).
Similarly, when a function is reflected over the y-axis, each point on the graph is flipped across the y-axis. This means that the x-coordinate of each point becomes its negative value. Mathematically, if (x, y) is a point on the original graph, then the corresponding point on the reflected graph is (-x, y).
If a function is reflected over the origin (0,0), each point on the graph is flipped across both the x-axis and the y-axis. This means that both the x-coordinate and the y-coordinate of each point become their negative values. Mathematically, if (x, y) is a point on the original graph, then the corresponding point on the reflected graph is (-x, -y).
Therefore, when we talk about the reflection of a function, we need to specify the reflection axis: x-axis, y-axis, or origin. The reflection axis determines the transformation of the function’s graph.
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