Question

3. A relation is graphed on the set of axes below. Based on this graph, the relation is (1) a function because it passes the horizontal line test (2) a function because it passes the vertical line test. (3) not a funotion beeause it fails the horizontal line test (4) not a function because it fails the vertical line test

Answer 1

The relation is (4) not a function because it fails the vertical line test.

Step-by-step explanation:

A function must pass the vertical line test, meaning that no vertical line intersects the graph at more than one point for every input value. In this case, if we draw vertical lines at various positions along the x-axis and those lines intersect the graph at more than one point, then the relation fails the vertical line test, indicating that it is not a function. Therefore, the correct answer is option (4).

Looking at the graph, suppose there exist some x-values that correspond to multiple y-values. When drawing vertical lines passing through these x-values, if any of these lines intersect the graph at more than one point (indicating multiple y-values for the same x-value), then it fails the vertical line test. This means the relation doesn't uniquely associate each input (x-value) with exactly one output (y-value), violating the definition of a function.

For instance, consider x-values of -1 and 2. If corresponding to these x-values, there are multiple y-values, then the graph would show points (-1, y1) and (2, y2) such that y1 ≠ y2. Drawing vertical lines through -1 and 2 would intersect the graph at more than one point, failing the vertical line test, hence concluding that the relation is not a function.

Answer 2

Based on this graph, the relation is `a function because it passes the vertical line test. `

The answer is option ⇒2

Step-by-step explanation:

Based on the graph provided, we can determine whether the relation is a function by applying the horizontal line test and the vertical line test.

The horizontal line test is used to check if any horizontal line intersects the graph more than once. If every horizontal line intersects the graph at most once, then the relation is a function.

The vertical line test is used to check if any vertical line intersects the graph more than once. If every vertical line intersects the graph at most once, then the relation is also a function.

By examining the graph, we can see that every vertical line intersects the graph at most once. Therefore, the relation passes the vertical line test and is a function.

However, if we observe the graph carefully, we can see that there are some horizontal lines that intersect the graph at more than one point. This means that the relation fails the horizontal line test.

Hence, based on the information provided, the correct answer is:

(2) a function because it passes the vertical line test.