Question

Write an equation that represents a vertical translation 7 units down of the graph of g(x)=|x|.

Answer 1

Answer: Ix+10I

Step-by-step 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.