Answer:
Only the function represented by graph 2 has an inverse function
Step-by-step explanation:
* Lets explain the inverse of the function
- The Function is a relation between x-coordinates and the y-
coordinates of the order pairs under the condition every
x-coordinate has only one y-coordinate
- Ex: R = {(2 , 3) , (1 , 5) , (-2 , -3)} is a function because every x-
coordinate has only one y-coordinate and R = {(2 , 3) , (-1 , 4) ,
(2 , 5)} not a function because the x-coordinate 2 has two y-
coordinates 3 and 5
- We use the vertical line to test the graph is function or not, if
the vertical line intersects the graph in one point then the
graph is function if intersects it in more than one point then the
graph is not function
- We have two types of function one-to-one function and
many-to-one function
# one-to-one function means every x-coordinate has only 1 y-coordinate
# many-to-one function means some x-coordinates have only 1
y-coordinate
- We find the inverse function by switching x and y, then one-to-
one function has inverse but many-to-one has not inverse
because when we switched x and y it will be one-to-many
means one x-coordinate has many y-coordinates and this is not
a function
- We use the horizontal line to test the graph of the function has
inverse or not, if the horizontal line intersects the graph in one
point then the function of the graph has inverse if it intersects
the graph in more than one point ,then the function of the
graph has no inverse
* Now lets test all the graphs by using the horizontal line
# graph 1
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 1 has no inverse
# graph 2
∵ The horizontal line cuts the graph in just 1 point
∴ The function of graph 2 has inverse
# graph 3
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 3 has no inverse
# graph 4
∵ The horizontal line cuts the graph in more than 1 point
∴ The function of graph 4 has no inverse
* Only the function represented by graph 2 has an inverse function
is autonomous
is *not* autonomous