Question

question 10
which of the following describes the end behavior of a graph?

telling where the graph is increasing or decreasing.
telling what the ends of the graph is doing.
the highest point of the graph.
the lowest point of the graph.

Explanation:

Define end behavior of a function

The end behavior of a graph describes what happens to the values of \(y\) (the function values) as \(x\) approaches positive infinity (\(x \to \infty\)) and negative infinity (\(x \to -\infty\)). In simple terms, it describes what the ends of the graph are doing as you move far to the left and far to the right.

Evaluate the given options

• Telling where the graph is increasing or decreasing: This describes intervals of increase and decrease, which occur in the middle domain of the function, not the extreme ends.
• Telling what the ends of the graph is doing: This directly matches the definition of end behavior (how the graph behaves at its far left and far right limits).
• The highest point of the graph: This describes the absolute maximum of the graph.
• The lowest point of the graph: This describes the absolute minimum of the graph.

Answer:

• Telling where the graph is increasing or decreasing.
• Telling what the ends of the graph is doing. (Correct answer)
• The highest point of the graph.
• The lowest point of the graph.