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

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  • Thread starter missnerdist
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In summary, the equation of y=x^3-x^2+x-1 after being reflected in both the y-axis and x-axis is y=-x^3+x^2-x+1.
  • #1
missnerdist
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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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  • #2
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]
 

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

What is the equation for "X^3-x^2+x-1 after being reflected?"

The equation for "X^3-x^2+x-1 after being reflected" is y = -x^3 + x^2 - x + 1.

What happens to the graph of "X^3-x^2+x-1 after being reflected?"

The graph of "X^3-x^2+x-1 after being reflected" is mirrored across the y-axis, resulting in a graph that is symmetrical about the y-axis.

How does the axis of symmetry change after reflecting "X^3-x^2+x-1"?

The axis of symmetry for "X^3-x^2+x-1" is the y-axis. After reflecting, the axis of symmetry remains the same.

What is the range of "X^3-x^2+x-1 after being reflected?"

The range of "X^3-x^2+x-1 after being reflected" is all real numbers, as the graph extends infinitely in both positive and negative y-directions.

How does the degree of the polynomial change after reflecting "X^3-x^2+x-1"?

The degree of the polynomial remains the same after reflecting "X^3-x^2+x-1." In this case, the degree is 3, as it is a cubic polynomial.

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