Power Functions Practice

1. Consider the polynomial function $q(x)=3x^4-5x^3-2x^2+x-18$.

   What is the end behavior of the graph of $q\ $?
   

   Choose 1 answer:

   1. $x \rightarrow \infty$, $q(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow \infty$.
   2. As $x \rightarrow \infty$, $q(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow \infty$.
   3. As $x \rightarrow \infty$, $q(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow -\infty$.

   4. As $x \rightarrow \infty$, $q(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow -\infty$.

2. Consider the polynomial function $g(x)=-x^4+2x^3+5x^2-1$.
   

   What is the end behavior of the graph of $g\ $?

   Choose 1 answer:

   1. As $x \rightarrow \infty$, $g(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $g(x) \rightarrow \infty$.
   2. As $x \rightarrow \infty$, $g(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $g(x) \rightarrow \infty$.
   3. As $x \rightarrow \infty$, $g(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $g(x) \rightarrow -\infty$.

   4. As $x \rightarrow \infty$, $g(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $g(x) \rightarrow -\infty$.

3. Consider the polynomial function $h(x)=3x^7+x^4+5x^3-80$.
   

   What is the end behavior of the graph of $h\ $?
   

   Choose 1 answer:

   1. As $x \rightarrow \infty$, $h(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $h(x) \rightarrow \infty$.
   2. As $x \rightarrow \infty$, $h(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $h(x) \rightarrow \infty$.
   3. As $x \rightarrow \infty$, $h(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $h(x) \rightarrow -\infty$.

   4. As $x \rightarrow \infty$, $h(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $h(x) \rightarrow -\infty$.

4. Consider the polynomial function $q(x)=-2x^8+5x^6-3x^5+50$.

   What is the end behavior of the graph of $q\ $?

   Choose 1 answer:

   1. As $x \rightarrow \infty$, $q(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow \infty$.
   2. As $x \rightarrow \infty$, $q(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow \infty$.
   3. As $x \rightarrow \infty$, $q(x) \rightarrow -\infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow -\infty$.
   4. As $x \rightarrow \infty$, $q(x) \rightarrow \infty$, and as $x \rightarrow -\infty$, $q(x) \rightarrow -\infty$.

Source: Khan Academy, https://www.khanacademy.org/math/algebra2/x2ec2f6f830c9fb89:poly-graphs/x2ec2f6f830c9fb89:poly-end-behavior/e/determine-the-end-behavior-of-polynomials
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