Question

In the following exercises, determine whether each graph is the graph of a function and if so, is it one-to-one:

(a)

(b)

Short answer

Part (a). The graph represents a function and it is also one-to-one.

Part (b). The graph represents a function but it is not one-to-one.

Step-by-step solution

Part (a) Step 1. Given Information 

The given graph is

We have to determine whether the graph is the graph of a function and if so, is it one to one.

Step 2. Use horizontal line test and vertical line test 

If every vertical line intersects the graph of a function in at most one point, it is a function.

If every horizontal line intersects the graph of a function in at most one point, it is a one-to-one function.

Let's apply both tests

By applying both the tests we get that the vertical line intersects the graph at most one point. Thus, the graph represents a function. The horizontal line intersects the graph at most one point thus, it is a one-to-one function.

Part (b) Step 1. Given Information 

The given graph is

We have to determine whether the graph is the graph of a function and if so, is it one to one.

Step 2. Use horizontal line test and vertical line test 

If every vertical line intersects the graph of a function in at most one point, it is a function.

If every horizontal line intersects the graph of a function in at most one point, it is a one-to-one function.

Let's apply both tests

By applying both the tests we get that the vertical line intersects the graph at most one point. Thus, the graph represents a function. The horizontal line intersects the graph at more than one point thus, it is not a one-to-one function.