Which function transforms the graph of y= x^2 so that it is first shifted down 4 units and its then reflected across the y- axis?
a. y= -x^2 +4
b. y= -x^2 - 4
c. y= ( -x)^2 -4
d. y= - ( x + 4 )^2

Option C. y= ( -x)^2 -4

Step-by-step explanation:

If we have a function and we want to transform it into a function g(x) that is equal to f(x) displaced c units down on the y-axis, then we must do:

In this case we want to move the function 4 units down, then:

Finally, to reflect the function on the y-axis. must do

Then we have the following function:

The answer is option C

its a straight line parallel to the time axis