So let's break this down.
We will start by using the basic representation of a function: y = x.
Absolute value equation looks like this: y = |x|.
Factor gives the coefficient of x: y = (5/7)x
Reflection across the x - axis means that x - negative: y = - x
When a function is shifting horizontally, subtracting from x is right and adding to x is left: y = x - 8
(If there is a y - intercept or a coefficient, put parenthesis around x and the horizontal shift: (x - 8).
When shifting up and down, add to the end of the equation to shift up and subtract to shift down: y = x + 11
(This one does not get parenthesis because it is the y intercept)
Put it all together: y = -(5/7)|(x-8)|+11
You technically don't have to put parenthesis in this scenario because the absolute value sign has the separation implied but if you are new to this, it's good practice.
Let me know if you have any questions!
