What type of transformation takes the graph of f(x) = |x| to the graph of g(x) = |4+x| a. vertical translation of 4 units down b. horizontal translation of 4 units left c. vertical translation of 4 units up d. horizontal translation of 4 units right

Adding a number to the variable moves the graph horizontally to the left.

The answer is B.

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

a: 1/6, j: 1/4

step-by-step explanation: you are welcome