# College Algebra Graded Homework #6

**Show your work on notebook paper. Record the final
answers onto this sheet.
Determine whether the function is a polynomial function . (Write YES or NO)**

**Find the degree of the polynomial function .**

f(x) is degree

**Find the x- intercepts of the polynomial function. State whether the graph crosses the x-axis, or touches the x-axis and**

turns around, at each intercept.

turns around, at each intercept.

**Find the y- intercept of the polynomial function.**

**Use the Leading Coefficient Test to determine the end behavior of the polynomial function. (You can explain the end**

behavior in words or draw a "picture box" illustrating the behavior at the ends.)

behavior in words or draw a "picture box" illustrating the behavior at the ends.)

11) A herd of moose is introduced to a wildlife refuge. The number of moose , N(t), after t years is described by the

polynomial function . Use the Leading Coefficient Test to determine the graph's end

behavior. Write a sentence to explain what this means about what will eventually happen to the moose

population?

**Find the zeros of the polynomial function.**

**Find the zeros for the polynomial function and give the
multiplicity for each zero . State whether the graph crosses the
x-axis or touches the x-axis and turns around, at each zero.**

**Write the equation of a polynomial function with the
given characteristics. Use a leading coefficient of 1 or -1 and make
the degree of the function as small as possible.**

15) Crosses the x-axis at -4, 0, and 1; lies above the x-axis between -4 and 0; lies below the x-axis between 0 and 1.

16) Suppose that a polynomial function is used to model the data shown in the graph below .

Determine the degree of the polynomial function of best
fit and the sign of the leading coefficient.

The polynomial will be degree with a
lead coefficient.

17) The profits (in millions) for a company for 8 years were as follows:

Which of the following polynomials is the best model for this data?

**Graph the polynomial function. Be sure to put an
appropriate scale on the graph. Label the x-intercepts and the
y-intercept.**

**Complete the following:
(a) Use the Leading Coefficient Test to determine the graph's end behavior.
(b) Find the x-intercepts. State whether the graph crosses the x-axis or touches
the x-axis and turns around at each
intercept.
(c) Find the y-intercept.
(d) Graph the function.**

** Divide using long division.**

**Divide using synthetic division .**

**Use synthetic division and the Remainder Theorem to
find the indicated function value .**

**Use synthetic division to show that the number given to
the right of the equation is a solution of the equation , then solve
the polynomial equation.**

The solutions are

**Use the graph or table to determine a solution of the equation. Use synthetic
division to verify that this number is a
solution of the equation. Then solve the polynomial equation.**

The solution(s) to the polynomial are

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