Question

1. determine whether the following graph represents a function.

a. not a function
b. function

1. determine whether the following graph represents a function.

a. not a function
b. function

1. fill in the blanks below in order to justify whether or not the mapping shown represents a function.

the mapping diagram above ______ a function since ____ in ____ has ____ ______

word bank 1: (a) does not represent, (b) represents
word bank 2: (a) each number, (b) one number
word bank 3: (a) set a (the input), (b) set a (the output), (c) set b (the output), (d) set b (the input)
word bank 4: (a) multiple mappings, (b) no mapping, (c) only one mapping
word bank 5: (a) from set a (the output), (b) from set a (the input), (c) to set b (the input), (d) to set b (the output)

1. which set of ordered pairs represents a function?

a. {(2, -5), (5, -5), (0, 5), (-4, 1)}
b. {(6, 0), (-4, 5), (0, 7), (6, 6)}
c. {(-3, 3), (-8, -6), (6, 0), (-3, 2)}
d. {(-7, 3), (-7, 8), (-4, -8), (1, -4)}

Explanation:

Question 3

Step1: Recall the vertical line test.

A graph represents a function if any vertical line drawn intersects the graph at most once. For the given graph, when we apply the vertical line test (e.g., at \(x = 0\)), the vertical line intersects the graph at more than one point.

Step2: Determine the result.

Since the vertical line test fails (multiple intersections at some \(x\)-value), the graph does not represent a function.

Step1: Apply the vertical line test.

For the given linear graph, any vertical line drawn will intersect the graph at exactly one point. This satisfies the definition of a function (each input \(x\) has exactly one output \(y\)).

Step2: Conclude the result.

Since the vertical line test is passed, the graph represents a function.

Step1: Recall the function definition for mappings.

A function is a mapping where each element in the domain (Set A, input) has exactly one mapping to the codomain (Set B, output). In the given mapping, the element \(-3\) in Set A (input) maps to both \(-4\) and \(7\) in Set B (output), so it has multiple mappings.

Step2: Fill in the blanks.

• Word bank 1: (a) does NOT represent (because of multiple mappings from an input).
• Word bank 2: (b) one number (the element \(-3\) is one number in Set A).
• Word bank 3: (a) Set A (the input) (since \(-3\) is in Set A, the input set).
• Word bank 4: (a) multiple mappings (as \(-3\) maps to two elements in Set B).
• Word bank 5: (b) from Set A (the input) (the multiple mappings are from the input set, Set A, to the output set, Set B).

So the mapping diagram above \(\boldsymbol{\text{does NOT represent}}\) a function since \(\boldsymbol{\text{one number}}\) in \(\boldsymbol{\text{Set A (the input)}}\) has \(\boldsymbol{\text{multiple mappings}}\) \(\boldsymbol{\text{from Set A (the input)}}\).

Answer:

A. Not a Function

Question 4