Graphing Polynomial Functions

A polynomial function has a root of -4 with multiplicity 4, a root of -1 with multiplicity 3, and a root of 5 with multistlicity 6. if the function has a positive leading coefficient and is of odd degree which could be the graph of the function?

B

At which root does the graph of f(x) = (x - 5)^3(x + 2)^2 touch the x-axis? A. -5 B. -2 C. 2 D. 5

B. -2

Which of the following graphs could be the graph of the function f(x)= -0.08x(x² - 11x + 18)? A B C D

C

Which graph has the same end behavior as the graph of f(x) = -3x^3 - x^2 + 1? A B C D

D

What is the end behavior of the graph of the polynomial function f(x) = 3x^6 + 30x^5 + 75x^4? A B C D

D. As x→−∞, γ→∞ and as x→∞, y→∞

Which graph shows the same end behavior as the graph of f(x) = 2x^6 - 2x^2 - 5? A B C D

NOT D TRY A

Which of the following graphs could be the graph of the function f(x) = x^4 + x^3 - x^2 - x? A B C D

A

At which root does the graph of f(x) = (x + 4)^6(x + 7)^5 cross the x-axis? A. -7 B. -4 C. 4 D. 7

A. -7

What is the end behavior of the graph of the polynomial function f(x) = 2x^3 - 26x - 24? A B C D

B. As χ→−∞, γ→−∞ and as χ→∞, γ→∞

Which statement describes the graph of f(x) = -x^4 + 3x^3 + 10x^2? A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5 and x = -2. B. The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = -2. C. The graph crosses the x-axis at x = 0 and touches the x-axis at x = -5 and x = 2. D. The graph touches the x-axis at x = 0 and crosses the x-axis at x = -5 and x = 2.

B. The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5 and x = -2.

Which of the following graphs could be the graph of the function f(x)= 0.03x²(x² - 25)? A B C D

A

which of the following graphs could be the graph of the function f(x)= 0.003x^2(x^2 - 25)

A.

Let a and b be real numbers where a ≠ b ≠ 0. Which of the following functions could represent the graph below? A. f(x) = x(x - a)^3(x - b)^3 B. f(x) = (x - a)^2(x - b)^4 C. f(x) = x(x - a)^6(x - b)^2 D. f(x) = (x - a)^5(x - b)

B. f(x)= (x-a)^2 (x-b)

Which statement describes the graph of f(x) = 4x^7 + 40x^6 + 100x^5? A. The graph crosses the x-axis at x = 0 and touches the x-axis at x = 5. B. The graph touches the x-axis at x = 0 and crosses the x-axis at x = 5. C. The graph crosses the x-axis at x = 0 and touches the x-axis at x = -5. D. The graph touches the x-axis at x = 0 and crosses the x-axis at x = -5.

C. The graph crosses the x-axis at x = 0 and touches the x-axis at x = -5.

A polynomial function has a root of -5 with multiplicity 3, a root of 1 with multiplicity 2, and a root of 3 with multiplicity 7. If the function has a negative leading coefficient and is of even degree, which statement about the graph is true? A. The graph of the function is positive on (−∞, -5). B. The graph of the function is negative on (-5, 3). C. The graph of the function is positive on (−∞, 1). D. The graph of the function is negative on (3, ∞).

D. The graph of the function is negative on (3, ∞).

Which statement describes the graph of f(x) = -4x^3 - 28x^2 - 32x + 64? A. The graph crosses the x-axis at x = 4 and touches the x-axis at x = -1. B. The graph touches the x-axis at x = 4 and crosses the x-axis at x = -1. C. The graph crosses the x-axis at x = -4 and touches the x-axis at x = 1. D. The graph touches the x-axis at x = -4 and crosses the x-axis at x = 1.

D. The graph touches the x-axis at x = -4 and crosses the x-axis at x = 1.