Power Functions Practice

Pactice Problems

It's time to practice determining the end behavior of power functions. Here are problems for you to try. Hints and videos are also available if you need help.

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 $x \rightarrow -\infty$ , $q(x) \rightarrow -\infty$ .
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 $x \rightarrow -\infty$ , $g(x) \rightarrow -\infty$ .
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 $x \rightarrow -\infty$ , $h(x) \rightarrow -\infty$ .
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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