Final Examination in Introduction to Algebra

A relation is a correspondence between two sets of values/elements called the domain and range, respectively. Which of the following statements best describes when a relation can be called a function?

• For each first coordinate, there is exactly one second coordinate.

• For each first coordinate, there is a corresponding odd coordinate.

• For every first element x, there are exactly two coordinates.

• For every first element x, there exists no irrational coordinate

Select the set of coordinates that DOES NOT belong to the group.

• {(1,2), (1,3), (1,4), (1,5)}

• {(2,3), (2,7), (3,4), (4,7)}

• {(1,5), (5,2), (1,7), (1,3)}

• {(2,0), (0,-2), (-2,-4), (-4,-6)}

Select the set of coordinates that illustrates a FUNCTION.

• {(0,1), (0,2), (3,5), (1,1)}

• {(1,2), (1,1), (1,4), (1,6)}

• {(2,7), (3,7), (4,3), (1,4)}

• {(3,2), (2,5), (3,1), (0.5,6)}

Which of the following illustrates a MERE RELATION?

• {(9,2), (8,7), (7,0), (6,5)}

• {(1,5), (4,6), (1,3), (8,5)}

• {(2,1), (5,7), (4,4), (3,1)}

• {(1,7), (2,3), (11,0), (4,5)}

Decide which of the following statements about the VERTICAL LINE TEST is TRUE.

• If the vertical line drawn across the graph of a function intersects the graph twice, then the graph represents a function.

• If the vertical line drawn across the graph of a function intersects the graph twice, then the graph does not represent a function.

• The vertical line test only works for x-values less than 0.

• The vertical line test only works for x-values more than 0.

Is this a function or relation?

{(1,3), (9,1), (2, 4), (5,4), (7,0)}

Is this a function or mere relation?

{(3,4), (1,7), (0, 4), (3,5), (3, 7)}

Is this a function or a mere relation?

{(1/2, 0), (-1, 3), (-2, 5), (-5, -2), (0, 0)}

Determine whether the function is injective, surjective, or bijective.

{(0, -1), (-1, -2), (-2, -3), (-3, -4), (-4, -5)}

Determine whether mere relation, injective, surjective, or bijective.

{(1,2), (-3,4), (1,1), (-1,-3), (0,1)}