Question

2026 (8 weeks) america castellanos 02/12/26 11:13 am
3.5): polynomial
question 1, 3.5.3
hw score: 0%, 0 of 8 points
points: 0 of 1
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graph the polynomial function.
$h(x) = -0.4x^9$
choose the correct graph below.
a.
b.
c.
d.

Explanation:

Step1: Analyze degree and leading coefficient

The function is $h(x) = -0.4x^9$. The degree (9) is odd, and the leading coefficient (-0.4) is negative. For odd-degree polynomials with negative leading coefficients: as $x\to+\infty$, $h(x)\to-\infty$; as $x\to-\infty$, $h(x)\to+\infty$.

Step2: Test key points

• When $x=0$, $h(0) = -0.4(0)^9 = 0$, so the graph passes through $(0,0)$.
• When $x=1$, $h(1) = -0.4(1)^9 = -0.4$, so the graph passes through $(1, -0.4)$.
• When $x=-1$, $h(-1) = -0.4(-1)^9 = 0.4$, so the graph passes through $(-1, 0.4)$.

Step3: Match to graph

The graph that rises as $x\to-\infty$, falls as $x\to+\infty$, and passes through the above points is option A.

Answer:

A. [Graph corresponding to option A]