Lesson Notes 6-2 Characteristics Of Polynomial Functions Answers printable pdf download

Lesson Notes 6-2 Characteristics Of Polynomial Functions Answers

Lesson Notes 6-2

Characteristics of Polynomial Functions

Last lesson we investigated polynomial functions by looking at a graph. In this lesson,

we are asked to match graphs to their equations as well as determine characteristics

without graphing. There are some important things to remember.

When a polynomial function is in standard form:

• The maximum number of x-intercepts the graph may have is equal to the degree

of the function.

• The maximum number of turning points the graph may have is equal to one less

than the degree of the function.

• The degree and leading coefficient indicate the end behaviour of the graph of the

function.

• The y-intercept of the graph is equal to the constant term of the function.

The standard form of polynomial functions can be written in the following ways:

• If linear, f(x) = ax + b

• If quadratic, f(x) = ax

+ bx + c

• If cubic, f(x) = ax

+ bx

+ cx + d

Linear and cubic polynomial functions have similar end behaviour.

• Negative leading coefficient: the graph extends from Quadrant II to Quadrant IV

• Positive leading coefficient: the graph extends from Quadrant III to Quadrant I

Quadratic polynomial function have a different end behaviour.

•Negative leading coefficient: the graph extends from Quadrant III to Quadrant IV

• Positive leading coefficient: the graph extends from Quadrant II to Quadrant I

In your descriptions of characteristics of a function we must include the number of x-

intercepts, the y-intercept, end behaviour, domain, range, and the number of possible

turning points.

Example 1: Determine the characteristics of each function, using only its equation.

a) f(x) = 4x + 2

(b) f(x) = -5x

+ 2x – 1

• degree:

• leading coefficient:

• constant term:

• number of x-intercepts:

• y-intercept:

• extends from Quad

to Quad

• domain:

• range:

• number of turning points:

Lesson Notes 6-2 Characteristics Of Polynomial Functions Answers