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

  • Thread starter Thread starter missnerdist
  • Start date Start date
AI Thread Summary
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.
missnerdist
Messages
6
Reaction score
0
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!
 
Mathematics news on Phys.org
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]
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
View full post »

Similar threads

B Strange quadratic manipulation
Replies
6
Views
2K
I Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
Replies
16
Views
587
B How Do You Derive the Formula for sin(x-y)?
Replies
5
Views
2K
I My attempt to understand horizontal transformations of functions
Replies
6
Views
2K
I Transforming coordinates between Cartesian and spherical
Replies
1
Views
2K
B Adding 'x' to 'xy' for Resultant <=1: A Table Guide
Replies
18
Views
2K
I Variant of Baker-Campbell-Hausdorff Formula
Replies
3
Views
2K
MHB Solving $x^3+y^3=7$ and $x^2+y^2+x+y+xy=4$ System of Equations
Replies
1
Views
1K
MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
Replies
1
Views
2K
MHB Reflecting B(3,-1) on Line g: 4y + x - 15 = 0
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top