Question

1. which of the following represent functions?

i.

input	output
5	0
6	-1
7	-1

ii.

input	output
4	6
6	4
8	2

iii.

input	output
1	1
1	2
2	3

a. all
b. i and ii
c. i and iii
d. ii and iii

1. determine whether the graph represents a function.

graph of a semicircle opening downward, with endpoints on the x - axis at (-6, 0) and (6, 0), and vertex at (0, 4)
a. the relation is not a function.
b. the relation is a function.

Explanation:

Question 10

Step1: Recall the definition of a function

A relation is a function if each input (x - value) has exactly one output (y - value).

Step2: Analyze Table I

• Inputs: 4, 5, 6, 7.
• For input 4, output is 0; input 5, output is 0; input 6, output is - 1; input 7, output is - 1.
• Each input has only one output. So, Table I represents a function.

Step3: Analyze Table II

• Inputs: 2, 4, 6, 8.
• For input 2, output is 8; input 4, output is 6; input 6, output is 4; input 8, output is 2.
• Each input has only one output. So, Table II represents a function.

Step4: Analyze Table III

• Inputs: - 2, 1, 1, 2.
• For input 1, we have two outputs: 1 and 2.
• Since one input (1) has more than one output, Table III does not represent a function.

So, Tables I and II represent functions.

Step1: Recall the vertical line test

A graph represents a function if no vertical line intersects the graph more than once.

Step2: Apply the vertical line test to the given graph

The given graph is a parabola opening downwards. If we draw a vertical line at any x - value, it will intersect the graph at most once.
So, the relation is a function.

Answer:

b. I and II

Question 11