a To determine if a graph shows a function, we can use the Vertical Line Test. If any vertical line we draw through the graph intersects it only once, the graph is a function.
Notice that both lines intersect the graph more than once. This graph fails the Vertical Line Test. Therefore, it does not represent a function.
b A function is a relationship where each x-value corresponds to exactly one y-value. If the x-values in the table are unique, we can conclude that each corresponds with only one y-value. Let's examine the table.
|c|c|
x & y
-3 & 19
5 & 19
19 & 0
0 & - 3
Looking at the x column, we can see that the values do not repeat. They are unique. Thus, each x corresponds with exactly one y. Therefore, the relationship is a function.
c As we did in Part B, we will check the table to see if the x-values are distinct. Let's look at the table.
|c|c|c|c|c|c|
x & 7 & - 2 & 0 & 7 & 4
y & 10 & 0 & 10 & 3 & 0
Examining the row that holds the x-values, we can see that x= 7 appears twice.
|c|c|c|c|c|c|
x & 7 & - 2 & 0 & 7 & 4
y & 10 & 0 & 10 & 3 & 0
Since x=7 is paired with two different y-values, the table does not show a function.
d Like in Part A, we can use the Vertical Line Test to determine if the graph represents a function.
Since any vertical line we could draw only crosses the graph once, the graph represents a function.
