Key Features of Graphs - 12/3

The interval of decrease is the range of x-values over which the function's output (f(x)) decreases. For example, if a function decreases from negative infinity to 2, the interval of decrease is (−∞, 2).

End behavior describes how the values of a function behave as x approaches positive or negative infinity. For example, if as x → -∞, f(x) → ∞, the graph rises indefinitely on the left side.

A maximum is the highest point on the graph of a parabola. If a parabola opens downwards, it has a maximum point.

A minimum is the lowest point on the graph of a parabola. If a parabola opens upwards, it has a minimum point.

The domain of a function is the set of all possible input values (x-values) for which the function is defined. For example, the domain [1, +∞) means the function is defined for all x starting from 1 to positive infinity.

A function is increasing on an interval if, as x increases, f(x) also increases. For example, if a function is increasing on the interval (-2.5, 2.5), then f(x) rises as x moves from -2.5 to 2.5.

The vertex is the highest or lowest point of a parabola, depending on its orientation. It is crucial for determining the maximum or minimum value of the function.

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.

The range of a function is the set of all possible output values (f(x)) that the function can produce.

The x-intercepts are found by setting f(x) = 0 and solving for x. These are the points where the graph crosses the x-axis.