Translate the parent absolute value function, y=|x|, left 6 and up 7. Write the equation of the next function.

Answer 1

y = |x+6| + 7

adding 7 shifts the function vertically up by 7 units

adding 6 to x shifts the function left horizonatlly by 6 units

original function y =|x| is V shaped with vertex = the origin = the minimum point

y= |x+6| + 7 is the same V shape but moved up 7 and left 6 units

It might help to graph the functions, plug in a couple points.

Answer 2

y = |x| ------> left 6 --------> y = |x+6|, since we want y to be = 0 when x = - 6

next we have:

y = |x+6| ------> up 7 --------> y = |x+6| + 7, since we want y to be = 7 when x = -6