Question

Which graphs are inverses of one another?

Answer 1

PURPLE AND ORANGE

its right on edge.

Answer 2

Answer: Choice B) purple and orange

The purple graph reflects over the line y = x to get the orange graph. Every point on the purple graph reflects over y = x using the rule (x,y) --> (y,x). So the x and y values swap places more or less.

We do not reflect over any horizontal line, which is why the blue and purple don't pair up as inverse pairs.

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The blue doesn't pair with the orange because of two reasons

1) The first local max, or highest hill, on the blue graph means that for some small region/interval, the y value is highest. However, the first bump in the orange graph shows that x is smallest for some y interval. The x and y swap when it comes to inverses.

2) The blue graph has y go off to negative infinity for both endpoints. So x must go off to negative infinity for the inverse (again x and y swap), but this isn't the case. Instead x goes off to positive infinity for both endpoints in the orange graph.