Hello!
This question is about which values you are changing when you are transforming an equation.
Let's go through the parent function for an absolute value equation and its various transformations.
Since we are only looking at horizontal and vertical transformations, we only need to worry about the c and d values.
The c value of a function determines a function's horizontal position, and the d value of a function determines a function's vertical position.
One thing to note here is that the c value is being subtracted from the x value, meaning that if the function is being transformed to the right, you would actually be subtracting that value, while the d value behaves like a normal value, if it is being added, the function is transformed up, and vice versa.
Now that we know this, let's write each expression.
a)
b)
c)
d)
Hope this helps!
