X^3-x^2+x-1 after being reflected?

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SUMMARY

The equation of the function y=x^3-x^2+x-1 after being reflected in both the y-axis and the x-axis is derived using the transformations for reflections. The reflection over the y-axis is represented by f(-x), and the reflection over the x-axis is represented by -f(x). Therefore, the combined transformation results in the equation y=-f(-x), which simplifies to y=-(-x)^3+(-x)^2-(-x)-1, yielding the final equation y=x^3+x-1.

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I'm not sure how to find the equation of y=x^3-x^2+x-1 after it is reflected in both the y-axis and x axis. Thank you!
 
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missnerdist said:
I'm not sure how to find the equation of y=x^3-x^2+x-1 after it is reflected in both the y-axis and x axis. Thank you!

reflection of $f(x)$ over the y-axis is $f(-x)$

reflection of $f(x)$ over the x-axis is $-f(x)$

so, $-f(-x)$ will do both ...

[DESMOS=-9.741235392320537,10.258764607679463,-10.137500000000001,9.862499999999999]y=x^3-x^2+x-1;y=\left(-x\right)^3-\left(-x\right)^2+\left(-x\right)-1;y=-\left(-x\right)^3+\left(-x\right)^2-\left(-x\right)+1[/DESMOS]
 

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