End Behavior and Increasing/Decreasing Intervals

Front

What is the definition of end behavior in a graph?

Back

End behavior refers to the behavior of the graph of a function as the input values (x) approach positive or negative infinity.

Front

How do you determine the end behavior of a polynomial function?

Back

To determine the end behavior of a polynomial function, analyze the leading term's degree and coefficient. If the degree is even, both ends of the graph will go in the same direction. If the degree is odd, the ends will go in opposite directions.

Front

What does it mean for a function to be increasing on an interval?

Back

A function is increasing on an interval if, for any two points in that interval, the function's value at the second point is greater than at the first point.

Front

What does it mean for a function to be decreasing on an interval?

Back

A function is decreasing on an interval if, for any two points in that interval, the function's value at the second point is less than at the first point.

Front

What is the significance of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce, which helps in understanding the behavior of the graph.

Front

How can you identify the end behavior of a rational function?

Back

To identify the end behavior of a rational function, analyze the degrees of the numerator and denominator. The end behavior is influenced by the leading coefficients and the degrees of these polynomials.

Front

What is the end behavior of the function f(x) = x^2 as x approaches -∞?

Back

As x approaches -∞, f(x) approaches ∞. The graph opens upwards.

Front

What is the end behavior of the function f(x) = -x^3 as x approaches ∞?

Back

As x approaches ∞, f(x) approaches -∞. The graph opens downwards.

Front

What is the relationship between the degree of a polynomial and its end behavior?

Back

The degree of a polynomial determines the direction of the ends of the graph. Even degrees lead to both ends going in the same direction, while odd degrees lead to opposite directions.

Front

How do you find the intervals where a function is increasing or decreasing?

Back

To find intervals of increase or decrease, take the derivative of the function, set it to zero to find critical points, and test intervals around those points.