Find the x- and y-intercepts of the polynomial function

Question

1) Form a polynomial whose real zeros and degree are given.

Zeros:
minus-44,
0,
11;
degree: 3
Type a polynomial with integer coefficients and a leading coefficient of 1.
f(x)equals=

2) Form a polynomial whose zeros and degree are given.

Zeros:
negative 3-3,
multiplicity 1;   
negative 4-4,
multiplicity 2; degree 3
Type a polynomial with integer coefficients and a leading coefficient of 1 in the box below.
f(x)equals=nothing

3. For the polynomial function below:

(a) List each real zero and its multiplicity.
(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(c) Determine the behavior of the graph near each x-intercepts.
(d) Determine the maximum number of turning points on the graph.
(e) Determine the end behavior; thatis, find the power function that the graph of f resembles for large values of |x|

f(x) = - 7(x - 4)(x + 5)^2

(Type each answer only once. Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

4. For the polynomial function below:

(a) List each real zero and its multiplicity.
(b) Determine whether the graph crosses or touches the x-axis at each x-intercept.
(c) Determine the behavior of the graph near eachx-intercept.
(d) Determine the maximum number of turning points on the graph.
(e)Determine the endbehavior, that is, find the power function that the graph of f resembles for large values of |x|

f(x) = -6(x^2 + 4)(x - 7)^3

5. Determine whether the graph could be the graph of a polynomial function. If it could be, list the real zeros and state the least degree the polynomial can have.

A. The graph shows a polynomial function. The real zero(s) is/are ______. The least degree the polynomial can have is _____.

B. The graph does not show a polynomial function.

6. Determine whether the graph could be the graph of a polynomial function. If it could be, list the real zeros and state the least degree the polynomial can have.

A. The graph shows a polynomial function. The real zero(s) is/are ___ . The least degree the polynomial can have is _____.

B. The graph does not show a polynomial function.

7. Decide which of the polynomial functions in the list might have the graph below.

a. y = -4x(x-1) (x-2)
b. y = x²(x-1)²(x-2)
c. y = 3x(x-1) (x-2)
d. y = x(x-1)² (x-2)²
e. y = 3x(1-x) (2-x)
f. y = -x(1-x) (x-2)

8. Find the following for the function f(x) = (x+5)² (x-4)²

(a) Find the x- and y-intercepts of the polynomial function f.
(b) Determine whether the graph of f crosses or touches the x-axis at each x-intercept
(c) Find the power function that the graph of f resembles for large values of |x|.
(d) Determine the maximum number of turning points on the graph of f.
(e) Determine the behavior of the graph of f near each x-intercept.
(f) Put all the irformation together to obtain the graph off.

9. Find the following for the function f(x) = 16x-x³.
(a) Find the x- and y-intercepts of the polynomial function f.
(b) Determine whether the graph of f crosses or touches the x-axis at each x-intercept. (c Find the power function that the graph of f resembles for large values of lxl.
(d) Determine the maximum number of turning points on the graph of f.
(e) Determine the behavior of the graph of f near each x-intercept.
(f) Put all the information together to obtain the graph of f.