End Behavior and Increasing/Decreasing

Front

What is end behavior in functions?

Back

End behavior describes the behavior of a function as the input values (x) approach positive or negative infinity. It indicates how the output values (y) behave in these limits.

Front

Define increasing interval in a function.

Back

An increasing interval is a range of x-values where the function's output (y) values are rising as x increases.

Front

Define decreasing interval in a function.

Back

A decreasing interval is a range of x-values where the function's output (y) values are falling as x increases.

Front

What does a turning point in a function represent?

Back

A turning point is a point on the graph of a function where the function changes from increasing to decreasing or vice versa.

Front

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

Back

The end behavior of a polynomial function can be determined by the leading term. If the leading coefficient is positive and the degree is even, both ends go up. If it's negative, both ends go down. If the degree is odd, one end goes up and the other goes down.

Front

What is the absolute minimum of a function?

Back

The absolute minimum is the lowest point on the graph of a function over its entire domain.

Front

How do you find the intervals of increase and decrease for a function?

Back

To find intervals of increase and decrease, take the derivative of the function, set it to zero to find critical points, and test intervals around these points to see where the function is increasing or decreasing.

Front

What does it mean if a function has a turning point at (a, b)?

Back

It means that at x = a, the function changes direction, either from increasing to decreasing or from decreasing to increasing, and the value of the function at this point is b.

Front

What is the significance of the leading coefficient in polynomial functions?

Back

The leading coefficient determines the direction of the end behavior of the polynomial function. A positive leading coefficient indicates that the function rises to the right, while a negative leading coefficient indicates that it falls to the right.

Front

How can you identify the intervals of a function that are increasing or decreasing from its graph?

Back

From the graph, intervals where the curve slopes upwards indicate increasing intervals, while intervals where the curve slopes downwards indicate decreasing intervals.