Lesson 3: ONE-TO-ONE AND ONTO FUNCTION

What is the Domain of the function below?

(-1,2) (5,7) (6,2) (-3,9) (4, 7) (8, -2)

• D= {-1, -3, 4, 5, 6, 8}

• D= {2, 5, 7, 9, 7, -2}

• D= {2, 7, 9, 7, -2}

• D= {-1, 5, 6, -3, 4, 8, 2, 7, 9, -2}

Given: A= {1, 2, 3, 5, 8} B= {4, 7, 9, 10, 11, 12} Which of the following is one-to-one but not onto function?. Suppose that we have a function mapping from set A to Set B.

• (1, 7) (2, 9) (3, 10) (5, 11) (8, 11)

• (1, 7) (2, 9) (3, 10) (5, 11) (8, 12)

• (1, 4) (2, 7) (3, 7) (5, 9) (8, 10)

• (1, 4) (2, 4) (3, 9) (5, 10) (8, 11)

Given: A= {1, 3, 5, 7, 9, 11) B= {2, 4, 6, 8, 10) Which of the following is onto but not one-to-one function?. Suppose that we have a function mapping from set A to Set B.

• (1, 2) (3, 4) (5, 6) (7, 8) (9, 10) (11, 10)

• (1, 2) (3, 4) (5, 6) (7,8) (9, 10) (11, 3)

• (1, 4) (3, 2) (5, 8) (7, 6) (9, 2) (11, 4)

• (1, 4) (3, 2) (5, 6) (7, 6) (9, 2) (11, 4)

Given: A= {2, 4, 6, 8, 10, 12} B= {1, 3, 5, 7, 9, 11} Which of the following is one-to-one and onto function?. Suppose that we have a function mapping from set A to Set B.

• (2, 1) (4, 1) (6, 3) (8, 5) (10, 7) (12, 9)

• (2, 3) (4, 1) (6, 5) (8, 5) (10, 7) (12, 9)

• (2, 1) (4, 5) (6, 3) (8, 7) (10, 11) (12, 9)

• (2, 1) (4, 5) (6, 3) (8, 7) (10, 11) (9,12)

Determine whether the following function is one-to-one.

f = {(1, 2), (3, 4), (5, 6), (8, 6), (10, -1) (11, 9) (12, -2)}

• The function is one-to-one because one unique element from its domain is assigned to an exactly one element in the co-domain.

• The function is one-to-one since the ordered pairs (5, 6) and (8, 6) have different first coordinates and the same second coordinate.

• The function is not one-to-one since the ordered pairs (5, 6) and (8, 6) have different first coordinates but has the same second coordinate.

• The function is not one-to-one because for every y, there is a unique x.

Check if the function g : R → R defined by g(x) = x² is an onto function or not.

• The function is onto function because every element in the co-domain is assigned to an element in the domain.

• The function is onto function because the range of the function is equal to the co-domain.

• The function is not onto function because not all elements of the co-domain is assigned to an element in the domain.

• The function is not onto function because there are elements in the domain that is assigned to more than one element in the co-domain.

If the graph of the function is said to be one-to-one then, the horizontal line test intersects the graph of the function_____?

• thrice

• twice

• once

• no point of intersection

Considering h:R→R, is h(x)=|x-4| a one to one function?

• The function is one to one because y-values are paired more than one x-values

• The function is not one to one because because y-values are paired with more than one x-values.

• The function is one to one because x-values are paired with exactly one y-value.

• The function is not one to one because x-values are paired with more than one y-values

• Real number greater than 7

• Real number less than 7

• Real number except 7.

• Real number except 0

Choose the correct statement(s)

A. If the horizontal line test intersects the graph of the function more than once, then the function is not one-to-one.

B. If the horizontal line test intersects the graph of the function once, then the function is one-to-one.

C. An onto function is a function whose image is equal to its codomain. Also, the range and domain of an onto function are equal.

D. An onto function is a function whose image is equal to its codomain. Also, the range and codomain of an onto function are equal.

• C only

• D only

• A,B and D

• A,B and C