A Polynomial Function Is a Function That Can Be Written in the Form

NAME: ______DATE: ______

MATHEMATICS 426

POLYNOMIAL FUNCTIONS

A polynomial function is a function that can be written in the form:

where and .

a)A function of the form , where , is called a ______function or a function of ______. It has a degree of ______. Its graph in the Cartesian plane is a ______. The basic constant function is ______.

The domain of a constant function is: ______

The range of a constant function is: ______

A constant function has ____ x-intercept, unless ______, in which case ______

______.

The y-intercept of a constant function, written in the above form, is ______.

The absolute maximum and the absolute minimum of a constant function are both the same, specifically ______. A constant function has _____ relative extremes.

Variation: A constant function is both increasing AND decreasing over _____ , but there are _____ intervals over which a constant function is either strictly increasing or strictly decreasing.

The sign of a function depends upon the ______. If ______, then the function is positive over ____ but is ______negative. If, however, ______, then the function is negative over ____ but is ______positive. In both these cases, there would be no difference between the intervals over which the function is positive or strictly positive, norbetween the intervals over which the function is negative or strictly negative. If ______, then the constant function is both positive AND negative over ____. The graph of such a function coincides with the ______. Thus, the equation of the ______is ______.

b)A function of the form , where and , is called a ______function or a ______. It has a degree of _____. Its graph in the Cartesian plane is an ______. The basic linear function is ______.

The domain of a linear function is: ______

The range of a linear function is: ______

The x-intercept of a linear function, written in the above form, is ______.

The y-intercept of a linear function, written in the above form, is ______. In the equation , the ____ parameter represents the ______or the ______of the function.

The “a” parameter of a linear function represents the ______or the ______

______of the function. If ______, then the function is ______

______. If ______, then the function is ______.

The sign of a linear function depends upon both the ______and on the ______. If ______, then the function is positive over ______and negative over ______. If ______, then the function is negative over ______and positive over ______.

A linear function has ____ extremes, neither absolute nor relative. This is clear from the ______of the function.

c)A function of the form , where and , is called a ______function or a ______. It has a degree of ______. Its graph in the Cartesian plane is a ______. The basic quadratic function is ______.

The coordinates of the vertex of the parabola defined by the above rule are ______.

The domain of a quadratic function is: ______

The range of a quadratic function is: ______if ______

______if ______

A quadratic function can have _____, ______, or ______zeros (x-intercepts).

The y-intercept of a quadratic function, written in the above form, is ______.

The variation of a quadratic function depends upon the ______of the _____ parameter, as well as the ___-value of the ______of the parabola. If ______, then the function decreases over the interval ______and increases over ______. If ______, then the function increases over the interval ______and decreases over ______.

A quadratic function will always have either an absolute ______or an absolute ______. The type of extreme that a quadratic function has is determined by the ______of the ____ parameter. If ______, then the function will have a ______but no ______. If ______, then the function will have a ______but no ______.

Write your own detailed summary describing the sign of a quadratic function. Be sure to consider all possible scenarios.