A graph is a function if an arbitrarily drawn vertical line only intersects the graph once. This is also know as the Vertical Line Test. Let's draw a few vertical lines and mark where they intersect the graph.
These lines all intersect the graph only once. Since it is impossible to draw a vertical line that intersects the graph more than once, the graph is a function.
b
To draw the inverse, we must reflect all of the points that fall on the function in the line y=x.
If it is a function, it must pass the vertical line test.
Since the vertical line intersects the graph three times, the inverse is not a function.
c
No it must not. If the graph of the inverse bends over itself it will not be a function.
d
As we talked about in Part C, if the graph of the inverse bends over itself it is not a function. We can determine if the inverse is a function by performing the Horizontal Line Test on the original function's graph. If the horizontal line intersects the function's graph more than once its inverse is not a function.
e
As we talked about in previous parts, any graph that fails the Vertical Line Test is not a function. However, its inverse is a function as long as it passes the Horizontal Line Test. Let's try to draw such a graph.
By drawing a vertical line, we can show that it is not a function. However, it does pass the horizontal line test which means its inverse must be a function.
