If you apply the changes below to the absolute value parent function, f(x) = |x|, what is the equation of the new function? Shift 8 units left. Shift 3 units down.

Answer 1

The rules for transforming a function f(x) into a function g(x) are:

g(x) = a·f(b(x-c)) + d where:

1. a = vertical dilation (stretch)
2. b = horizontal dilation (stretch)
3. c = horizontal (left/right) shift
4. d = vertical (up/down) shift

For f(x) = |x| it's:

g(x) = a·|b(x-c)| + d

There is no vertical or horizontal dilation, so a = b = 1. Shift 8 units left means c = -8. Shift 3 units down means d = -3.

g(x) = |x - (-8)| + (-3) = |x+8| - 3

Answer 2

New function is f(x+8) - 3 = |x+8| -3

Answer 3

The parent function is: f(x) = |x| Let's call this function f(x)

To have a function, let's call it g(z), that is "shifted 8 units left) means that gz) = f(x-8). For example, consider f(0) = ||0| = 0 and g(0-8) = |8-8| = |0| = 0. For any value of z, we write that as g(z) = |x-8|.

Now, to shift "3 units down," the value of g(x) = f(x)-3. That is, for every x, g(x) is 3 units less than f(x).

Final result for new function g(x):

g(x) = f(x-8) - 3