Question

Write an equation that represents a horizontal translation 10 units left of the graph of g(x) = |x|

Answer 1

Answer:  h(x) = |x+10|

---------------------------------------------------------

Explanation:

To shift the graph 10 units to the left, we replace x with x+10. What's really going on is that the xy axis shifts 10 units to the right (because x is now x+10; eg, x = 2 ---> x+10 = 2+10 = 12) so it appears that the graph is moving to the left. The general rule is h(x) = g(x+10). 

So,
g(x) = |x|
g(x+10) = |x+10| ... every x has been replaced with x+10
h(x) = g(x+10)
h(x) = |x+10|

We can use a graphing tool like GeoGebra to visually confirm we have the right answer (see attached). Note how a point like (0,0) on the green graph moves to (-10,0) on the red graph. 

Answer 2

To move a graph c units to the right, minus c from every x
to move a graph c units to the left, add c to every x

g(x)=|x|
move to left 10 units
add 10 to every x
h(x)=|x+10| is the equation of g(x) translated 10 units to the left