Question

The graph shows a polynomial function f(x) of degree 3.

Which statement about f(x) is true?
A
B
C
D
1(x) = (x-1)²(x+2)
f(x) = (x+1)²(x-2)
f(x) = (x+2)²(x-1)
f(x) = (x-2)(x+1)
-3
-2
-1
10
8
kok
6
4
2
o
-2
+
-6
2

Answer 1

Graph shows a cubic function with roots at -3, 1, and 4. Analyzing answer choices, only D (f(x) = (x - 2)(x - 1)(x + 3)) has these roots, matching the graph.Thus the correct expression is D.

The graph depicts a cubic polynomial function, f(x), with three roots, corresponding to the x-intercepts at roughly -3, 1, and 4.

Determining the correct expression for f(x) requires factoring a polynomial of degree 3. Analyzing the answer choices:

A. f(x) = (x - 1)(x + 2): This quadratic expression only has two roots, at x = 1 and -2, and doesn't match the graph's three roots.

B. f(x) = (x + 1)(x - 2): Similar to choice A, this quadratic expression only has two roots, at x = -1 and 2, and doesn't capture the three roots of the graph.

C. f(x) = (2 + 2)(x - 1): This simplifies to a linear function, f(x) = 4x - 4, which has only one root at x = 1 and doesn't reflect the cubic nature of the graph.

D. f(x) = (x - 2)(x - 1)(x + 3): This cubic expression, with factors corresponding to the three roots at -3, 1, and 4, accurately represents the graph of f(x).

Therefore, based on the factored form with roots at -3, 1, and 4, D. f(x) = (x - 2)(x - 1)(x + 3) is the true statement about the polynomial function in the graph.

So,D is the correct expression.