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 x1 and x2 in that interval, if x1 < x2, then f(x1) > f(x2).

Front

What is concavity in relation to a function's graph?

Back

Concavity refers to the direction the graph of a function curves. A function is concave up if its graph opens upwards, and concave down if it opens downwards.

Front

How do you determine the points of inflection of a function?

Back

Points of inflection occur where the function changes concavity, which can be found by analyzing the second derivative of the function.

Front

What is the inverse of a function?

Back

The inverse of a function f, denoted as f^{-1}, is a function that reverses the effect of f. If f(a) = b, then f^{-1}(b) = a.

Front

How do you find the inverse of a function graphically?

Back

To find the inverse graphically, reflect the graph of the function across the line y = x.

Front

What is the significance of the degree of a polynomial function?

Back

The degree of a polynomial function indicates the highest power of the variable in the function, which affects the function's behavior and the number of roots.

Front

What is the relationship between the degree of a polynomial and its number of turning points?

Back

A polynomial of degree n can have at most n-1 turning points.

Front

What is a point of inflection?

Back

A point of inflection is a point on the graph of a function where the curvature changes from concave up to concave down or vice versa.

Front

How do you determine the least possible degree of a polynomial given its behavior?

Back

The least possible degree can be determined by analyzing the number of roots and turning points the polynomial must have based on the given conditions.

Front

What is the relationship between increasing functions and their inverses?

Back

If a function is increasing, its inverse will also be increasing.