Consider the polynomial function h(x)=x^(6)-3x^(5)-17x^(3). What is the end behavior of the graph of h ? Choose 1 answer: (A) As x rarr oo,h(x)rarr oo, and as x rarr-oo, h(x)rarr oo. (B) As x rarr oo, h(x)rarr-oo, and as x rarr-oo,h(x)rarr oo. (C) As x rarr oo, h(x)rarr-oo, and as x rarr-oo,h(x)rarr-oo. (D) As x rarr oo,h(x)rarr oo, and as x rarr-oo, h(x)rarr-oo.

Identify Leading Term: The problem asks us to determine the end behavior of the graph of the polynomial function h(x) = x^6 - 3x^5 - 17x^3. To do this, we need to consider the leading term of the polynomial, as it dictates the end behavior of the graph.Analyze Leading Coefficient: The leading term of h(x) is x^6. The coefficient of this term is positive, and the degree is even. The end behavior of polynomial functions is determined by the leading term. For even-degree polynomials with a positive leading coefficient, as x approaches infinity, the function approaches infinity, and as x approaches negative infinity, the function also approaches infinity.Determine End Behavior: Therefore, based on the leading term x^6, we can conclude that as x approaches infinity (x → ∞), h(x) approaches infinity (h(x) → ∞), and as x approaches negative infinity (x → -∞), h(x) also approaches infinity (h(x) → ∞). This matches option (A) in the given choices.

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Consider the polynomial function h(x)=x^(6)-3x^(5)-17x^(3).
What is the end behavior of the graph of h ?
Choose 1 answer:
(A) As x rarr oo,h(x)rarr oo, and as x rarr-oo, h(x)rarr oo.
(B) As x rarr oo, h(x)rarr-oo, and as x rarr-oo,h(x)rarr oo.
(C) As x rarr oo, h(x)rarr-oo, and as x rarr-oo,h(x)rarr-oo.
(D) As x rarr oo,h(x)rarr oo, and as x rarr-oo, h(x)rarr-oo.

Consider the polynomial function $h(x)=x^{6}-3x^{5}-17x^{3}$ . $\newline$ What is the end behavior of the graph of $h$ ? $\newline$ Choose $1$ answer: $\newline$ (A) As $x \rightarrow \infty, h(x)\rightarrow \infty$ , and as $x \rightarrow -\infty, h(x)\rightarrow \infty$ . $\newline$ (B) As $x \rightarrow \infty, h(x)\rightarrow -\infty$ , and as $x \rightarrow -\infty, h(x)\rightarrow \infty$ . $\newline$ (C) As $x \rightarrow \infty, h(x)\rightarrow -\infty$ , and as $x \rightarrow -\infty, h(x)\rightarrow -\infty$ . $\newline$ (D) As $x \rightarrow \infty, h(x)\rightarrow \infty$ , and as $x \rightarrow -\infty, h(x)\rightarrow -\infty$ .

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Algebra 1

Compare linear and exponential growth

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Q. Consider the polynomial function

h(x)=x^{6}-3x^{5}-17x^{3}

\newline

What is the end behavior of the graph of

h

\newline

Choose

1

answer:

\newline

(A) As

x \rightarrow \infty, h(x)\rightarrow \infty

, and as

x \rightarrow -\infty, h(x)\rightarrow \infty

\newline

(B) As

x \rightarrow \infty, h(x)\rightarrow -\infty

, and as

x \rightarrow -\infty, h(x)\rightarrow \infty

\newline

x \rightarrow \infty, h(x)\rightarrow -\infty

, and as

x \rightarrow -\infty, h(x)\rightarrow -\infty

\newline

(D) As

x \rightarrow \infty, h(x)\rightarrow \infty

, and as

x \rightarrow -\infty, h(x)\rightarrow -\infty

Identify Leading Term: The problem asks us to determine the end behavior of the graph of the polynomial function $h(x) = x^6 - 3x^5 - 17x^3$ . To do this, we need to consider the leading term of the polynomial, as it dictates the end behavior of the graph.
Analyze Leading Coefficient: The leading term of $h(x)$ is $x^6$ . The coefficient of this term is positive, and the degree is even. The end behavior of polynomial functions is determined by the leading term. For even-degree polynomials with a positive leading coefficient, as $x$ approaches infinity, the function approaches infinity, and as $x$ approaches negative infinity, the function also approaches infinity.
Determine End Behavior: Therefore, based on the leading term $x^6$ , we can conclude that as $x$ approaches infinity ( $x \rightarrow \infty$ ), $h(x)$ approaches infinity ( $h(x) \rightarrow \infty$ ), and as $x$ approaches negative infinity ( $x \rightarrow -\infty$ ), $h(x)$ also approaches infinity ( $h(x) \rightarrow \infty$ ). This matches option $(A)$ in the given choices.