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

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To find the equation of y=x^3-x^2+x-1 after reflecting it over both the y-axis and the x-axis, first reflect over the y-axis by substituting -x for x, resulting in y=(-x)^3-(-x)^2-(-x)-1. This simplifies to y=-(-x)^3+(-x)^2-(-x)+1. The final equation after both reflections is y=x^3-x^2+x+1. Thus, the reflected function is y=x^3-x^2+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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