Answer
a) It is a function, and it is one-to-one.
b) It is a function, and it is not one-to-one.
c) It is not a function and it is not one-to-one.
d) It is not a function and it is not one-to-one.
Work Step by Step
To find out if a graph is a function, one must apply the vertical line test. If the graph is a function, one can apply the horizontal line test to see if it is one-to-one.
a) Applying the vertical line test shows that it only intersects one point in all of its domain. Thus, it is a function.
Applying the horizontal line test shows that it only intersects one point in all of its range. Thus, it is one-to-one.
b) Applying the vertical line test shows that it only intersects one point in all of its domain. Thus, it is a function.
Applying the horizontal line test shows that it intersects more than one point in all of its range. Thus, it is not one-to-one.
c) Applying the vertical line test shows that it intersects more than one point in all of its domain. Thus, it is not a function. Since it is not a function, it is not one-to-one.
d) Applying the vertical line test shows that it intersects more than one point in all of its domain. Thus, it is not a function. Since it is not a function, it is not one-to-one.
