What does the transformation f(x)↦f(-x) do to the graph of f(x)?
1 answer:
The function will simply get reflected about the y-axis.
Let's approach this through what we know. Since we know that the x values are mirrored, we know that the points in Quadrant I and IV will be reflected over to the negative side, Quadrants II and III, because they simply change in signs.
However, we also know that the function y-values do not change. This is because whatever the x values are don't change the range and y-values of an even function.
To be more specific, if we have an even function, we are most likely dealing with quadratics or variants/transformations of the quadratic function.
If we were to have 2, and -2, and we wanted to plug them into the equation:
, the signs do not change the y-values of the function.
Hence, we know that it ONLY gets reflected across the y-axis.
Let's approach this through what we know. Since we know that the x values are mirrored, we know that the points in Quadrant I and IV will be reflected over to the negative side, Quadrants II and III, because they simply change in signs.
However, we also know that the function y-values do not change. This is because whatever the x values are don't change the range and y-values of an even function.
To be more specific, if we have an even function, we are most likely dealing with quadratics or variants/transformations of the quadratic function.
If we were to have 2, and -2, and we wanted to plug them into the equation:
Hence, we know that it ONLY gets reflected across the y-axis.
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