Question

URGENT 20 POINTS Select each graph that shows a function and its inverse.

Answer 1

Answer: Graph first and fourth.

Step-by-step explanation:

If a function is reflected through line y=x,, we obtained an inverse function of that function.

In first graph,

The function is reflected through line y = x,

Hence, in this graph we obtained inverse functions.

In second graph,

The function is shifted horizontally,

This is why we did not get an inverse function.

In third graph,

The function is reflected through x-axis,

This is why we did not get the inverse of the function.

In fourth graph,

The function is reflected through line y = x,

Hence, in this graph we obtained inverse functions.

Answer 2

Graphically, two functions are inverses when either...

1) You can reflect the graph the graph about y = x.

2) The graph is the same if you switch the x and y axes.

Let's look at the graphs from left to right, call them 1, 2, 3, 4.

#1 is a reflection across that diagonal - so this is an inverse pair.

#2 is a reflection across the y - axis - not an inverse pair.

#3 is a reflection across the x - axis - not an inverse pair.

#4 is a reflection across the line y = -x - not an inverse pair as you change the signs while swapping the axes.

Thus graph #1 (the left most) is the inverse pair.