Key Features of Graphs

Front

What is the end behavior of the graph if as x→ -∞, y→ -∞ and as x→ +∞, y→ -∞?

Back

The graph decreases without bound as x approaches negative infinity and approaches a horizontal asymptote as x approaches positive infinity.

Front

What is the interval of increase for a function that increases from (1, +∞)?

Back

The function is increasing for all x values greater than 1.

Front

What does the vertical line test determine about a graph?

Back

The vertical line test determines if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the domain of a graph that is defined from -3 to 2, inclusive?

Back

The domain is [-3, 2], meaning the function includes all x values from -3 to 2.

Front

What does it mean if a graph fails the vertical line test?

Back

If a graph fails the vertical line test, it means that there are repeating input values, indicating that it is not a function.

Front

Define 'end behavior' in the context of graphing functions.

Back

End behavior describes the behavior of the graph as x approaches positive or negative infinity.

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What is the significance of arrows on a graph?

Back

Arrows indicate that the graph continues indefinitely in that direction.

Front

How do you determine the interval of decrease for a function?

Back

The interval of decrease is found by identifying the x-values where the function's output values are decreasing.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as x increases, the function's output values also increase.