Q37. - Algebra 2

Question

SPORTS For Exercises $35-37$, use the table that shows the leading home run and runs batted in totals in the American League for $1996-2000$

$37.$ Does the graph represent a function? Explain your reasoning.

Step-by-Step Solution

Answer

The graph does not represent a function.

Step 1 – Vertical line test.

The graph represents a function if no vertical line intersects the graph on more than one point. The graph does not represent a function if some vertical line intersects the graph on two or more points.

Step 2 – Given information.

The table shows the leading home runs and runs batted in totals in the American League for 1996-2000.

Step 3 – Graph of the given data.

Plot the data points on a coordinate plane from the given table.

Step 4 – Check whether the graph is a function or not.

Draw a vertical line on the above graph as shown below:

The above graph does not pass the vertical line test because the red vertical passes through the two points of the relation. For $x=56$ there exist two $y$-values $147 and 157$.

 Thus, the graph does not represent a function.