Question

question 1-2
selected response: 1 point for correct answer only.
examine the polynomial function f(x) graphed below.
which of the following is not a characteristic of the function f(x)?
the range of f(x) is (-infty, infty).
(x + 6) is the factor of f(x).
x = 3 is a triple root of the function.
as x \to +infty, f(x) \to -infty.

Explanation:

1. Range check: The graph extends upward to $+\infty$ and downward to $-\infty$, so the range is $(-\infty, \infty)$; this statement is true.
2. Factor check: The graph crosses the x-axis at $x=-6$, so $(x+6)$ is a factor of $f(x)$; this statement is true.
3. Root multiplicity check: The graph touches and turns around at $x=3$, which means this is a root with even multiplicity (not triple, which is odd); this statement is false.
4. End behavior check: As $x \to +\infty$, the graph points downward, so $f(x) \to -\infty$; this statement is true.

We need the statement that is NOT a characteristic, so we select the false one.

Answer:

$\boldsymbol{x = 3}$ is a triple root of the function.