How do you use the horizontal line test to determine whether the function #g(x)=abs(x+4)-abs(x-4)# is one to one?

1 Answer
Somebody N.
Oct 27, 2017

See below.

Explanation:

The horizontal line test just proves that if the line intersects the function graph in more than one place then the function is not one to one. The horizontal line is drawn anywhere it could intersect in more than one place, if there is such a place.

The first step is to plot the function. Then observe to see where a horizontal line could be placed to intersect at more the one point on the functions graph.

The graph below show that the lines #y=8# and #y=-8# both intersect the graph of #y = |4+x|-|4-x|# in an infinite number of places. So this function is not one to one it is a many to one function.

Graph:

enter image source here

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