Key Features of Graphs - 12/3

Front

What is the interval of decrease for a function?

Back

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).

Front

What does end behavior of a graph refer to?

Back

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.

Front

What is a maximum in the context of a parabola?

Back

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

Front

What is a minimum in the context of a parabola?

Back

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

Front

How do you determine the domain of a function?

Back

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.

Front

What does it mean for a function to be increasing?

Back

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.

Front

What is the significance of the vertex in a parabola?

Back

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.

Front

What is the difference between open and closed intervals?

Back

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

Front

What is the range of a function?

Back

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

Front

How do you find the x-intercepts of a graph?

Back

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.