First, let’s look at the parent function. The parent function is the original function in which changes are made to create a new function.
The parent function is
y=|x|
The changes made to make the function in the question is the function will be translated down 1 unit, hence why -1 trails behind the absolute value bars. So, this simply means all y-values of the function will be translated down 1 unit, and the x-values stay the same since the -1 only affects the y-values.
So, let’s graph y=|x| and simply subtract 1 from every output (y-value):
Remember, we must input an x-value into the function, and the function will manipulate this value to get an output value (y-value).
Let’s create a list of x and y values according to the parent function:
x=0
y=|0|——>y=0
Coordinate: (0, 0)
x=-1
y=|-1|——>y=1
Coordinate: (-1, 1)
x=-2
y=|-2|——>y=2
Coordinate: (-2, 2)
x=1
y=|1|—->1
Coordinate: (1, 1)
x=2
y=|2|——>2
Coordinate: (2, 2)
When we graph the ordered pairs, the function will intercept the origin and appear like a “V.” Now, the modified function has the trailing -1, indicating we must subtract 1 from the y-coordinates. Let’s create a new table of values to see this:
x=-2
y=|-2|-1 ——>y=2-1—>y=1
Coordinate: (-2, 1)
Recall that in the parent function, when x=-2, y=2. Now, when x=-2, y=1, so the y-coordinate is translated down 1 unit.
x=-1
y=|-1|-1 ——> y=1-1 —-> y=0
Coordinate: (-1, 0)
x=0
y=|0|-1 ——>y=-1
Coordinate: (0, -1)
x=1
y=|1|-1 ——> y=1-1 ——> y=0
Coordinate (1, 0)
x=2
y=|2|-1 ——> y=2-1 ——> y=1
Coordinate: (2, 1)
So, if you compare the modified function with the parent function, the x-values Eemian untouched, while the y-values are shifted down 1 unit. This is what the -1 does to the function. The -1 is outside the absolute value box meaning it affects the y-coordinates. The -1 would have to be subtracting the x to affect the x-coordinates.
So, the answer is graph B.)