Use matrices to determine the coordinates of the vertices of the reflected figure. then graph the pre-image and the image on the same coordinate grid. (picture provided)

The coordinates of the vertices of the reflected figure are :

R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6) ⇒ the right answer is (d)

Step-by-step explanation:

* When you reflect a point across the line y = x, the x-coordinate

 and y-coordinate change their places.

- If the point is (x , y) then its image is (y , x)

* If you reflect over the line y = -x, the x-coordinate and y-coordinate

 change their places and their signs

- If the point is (x , y) then its image is (-y , -x)

* Lets study the matrix of the reflection  about the line y = x

- The matrix of the reflection about the line y = x is

- Because the x-coordinate and y-coordinate change places.

* Now lets solve the problem

- We will multiply the matrix of the reflection about y = x

 by each point to find the image of each point

- The dimension of the matrix of the reflection about y = x

 is 2×2 and the dimension of the matrix of each point is 2×1,

 then the dimension of the matrix of each image is 2×1

∵ The point R is (-2 , 5)

∴

∴ R' is (5 , -2)

∵ The point S is (5 , 3)

∴

∴ S' is (3 , 5)

∵ The point T is (6 , -7)

∴

∴ T' is (-7 , 6)

* Lets look to the figures to find the right answer

∵ The R' is (5 , -2) , S' is (3 , 5) , T' is (-7 , 6)

∴ The right answer is (d)

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1