The transformed function is:
g(x) = -f(x) - 5
Which equation shows the transformed function?
We can see that the function f(x) has an y-intercept at 0, and a slope of 1, so this is just the parent linear function:
f(x) = x
In the other hand, we can see that g(x) has a slope of -1, and an y-intercept of -5, so we have:
A reflection over the x-axis, followed by a translation of 5 units down, this is written as:
g(x) = -x - 5 = -f(x) - 5