Write the absolute value equation given the transformations shifts right 5 units
shifts up 2 units
is reflected
is stretched by 0.5

y = - 0.5 | x - 5 | + 2

Step-by-step explanation:

g(x) = |x|

step - shifts right 5 units: g(x + 5) = | x - 5 |

step - shifts up 2 units: g(x + 5) + 2 = | x - 5 | + 2

step - reflected: - g(x + 5) + 2 = - | x - 5 | + 2

step - stretched by 0.5: y = - 0.5 | x - 5 | + 2

y = - 0.5 | x - 5 | + 2

since your problem is x^4 = 81, what you have to undeo is the "to the fourth power" part.

the inverse (opposite operation) of "to the fourth power" is "to the fourth root".

  (x^4) ^ ¼   = 81 ^ ¼  

  81 = 3^4     so (3 ^ 4) ^ ¼   =   3 ^ 1   = 3

by hand: (3 ^ 4) ^ ¼   =   3 ^ (4 x ¼) = 3 ^ 1   = 3   (when you take a power to a power, multiply the exponents.)

or, do it by calculator. one way of finding the fourth root is to use ^ (1/4)

step-by-step explanation: