Reference no: EM131216659
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.
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