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Choose any false statements regarding the graph.

enter image description here

Select all that apply.

(a) The graph is a function that has an inverse function.

(b) The graph is a function.

(c) The graph is a function that does not have an inverse function.

(d) The graph passes the horizontal line test.

(e) The graph is a one-to-one function.

(f) The graph passes the vertical line test.

I assumed that

The false statements are:

The graph is a one-to-one function.

The graph is a function that has an inverse function.

The graph passes the horizontal line test.

but not sure

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Yes, the false statements are a,d, and e. The others are true.


You need two facts here:

1) A graph passes the vertical line test (every vertical line intersects the graph in at most one point) if and only if the graph represents a function.

2) If we know that a graph represents a function, these three statements are equivalent (any one is true if and only if another one is true):

a) The graph passes the horizontal line test (every horizontal line intersects the graph in at most one point);

b) The function is one-to-one;

c) The function has an inverse function.


Looking at your graph, we see that every vertical line intersects the graph exactly once, so it passes the vertical line test. Therefore by the first fact we know the graph represents a function. So (b) and (f) are true.

We see that the horizontal line $y=6$ intersects the graph seven times that we can see and perhaps infinitely many times that we do not see, so it fails the horizontal line test. That means that by the second fact, (a), (d), and (e) are false. Item (c) is the opposite of (a), so (c) is true.

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  • $\begingroup$ yes please more details thanks $\endgroup$ – user155971 Feb 21 '15 at 18:38
  • $\begingroup$ @user155971: See the additions to my answer. $\endgroup$ – Rory Daulton Feb 21 '15 at 19:49
  • $\begingroup$ thank you sir for helping me $\endgroup$ – user155971 Feb 21 '15 at 19:56

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