Skip to main content

Math Trailhead

Reed College Department of Mathematics & Statistics

Print preview

Paper size
Additional printing options
Print headers
Print footers

Worksheet Polynomial Functions

6.

Determine the end behavior of the following polynomial function:
🔗
\begin{equation*} f(x) = 6 x^{11} + 15 x^{4} - 4 x^{15} + 30 x^{19} + 16 \end{equation*}
🔗
The leading term of the polynomial is
🔗
The degree of \(f(x)\) is
🔗
The leading coefficient is
🔗
The end behavior of the polynomial \(f(x)\) is of the form:
🔗
where:
🔗
Answer 1.
\(30x^{19}\)
🔗
🔗
Answer 2.
\(19\)
🔗
🔗
Answer 3.
\(30\)
🔗
🔗
Answer 4.
\(\text{C}\)
🔗
🔗
🔗

7.

Determine the end behavior of the following polynomial function:
🔗
\begin{equation*} f(x) = 14 - 4 x^{2} + 14 x^{8} + 10 x^{15} \end{equation*}
🔗
The leading term of the polynomial is
🔗
The degree of \(f(x)\) is
🔗
The leading coefficient is
🔗
The end behavior of the polynomial \(f(x)\) is of the form:
🔗
where:
🔗
Answer 1.
\(10x^{15}\)
🔗
🔗
Answer 2.
\(15\)
🔗
🔗
Answer 3.
\(10\)
🔗
🔗
Answer 4.
\(\text{C}\)
🔗
🔗
🔗

8.

Given \(f(x) = (x-9)(x + 7)(x + 5)\text{,}\) find the roots in increasing order.
🔗
The roots are , , and .
🔗
To the left of the first root, is the graph of \(f(x)\) above or below the x-axis? Answer above or below: .
🔗
Between the first two roots, is the graph of \(f(x)\) above or below the x-axis? Answer above or below: .
🔗
Between the last two roots, is the graph of \(f(x)\) above or below the x-axis? Answer above or below: .
🔗
After the last root, is the graph of \(f(x)\) above or below the x-axis? Answer above or below:
🔗
Answer 1.
\(-7\)
🔗
🔗
Answer 2.
\(-5\)
🔗
🔗
Answer 3.
\(9\)
🔗
🔗
Answer 4.
🔗
Answer 5.
🔗
Answer 6.
🔗
Answer 7.
🔗
🔗

15.

For \(f(x) = {4x^{3}\mathopen{}\left(3x-4\right)}\text{,}\) determine the `x`-intercepts and the end behavior. Enter intercepts as a comma separated list of points.
🔗
Intercepts :
🔗
🔗
Inputting the function into the Desmos graphing tool below may help investigate the function.
🔗
Answer 1.
\(\left(0,0\right), \left(1.33333,0\right)\)
🔗
🔗
Answer 2.
\(\infty \)
🔗
🔗
Answer 3.
\(\infty \)
🔗
🔗
🔗

16.

For \(f(x) = {-4x^{3}\mathopen{}\left(-2x-6\right)}\text{,}\) determine the `x`-intercepts and the end behavior. Enter intercepts as a comma separated list of points.
🔗
Intercepts :
🔗
🔗
Inputting the function into the Desmos tool below may help investigate the function.
🔗
Answer 1.
\(\left(0,0\right), \left(-3,0\right)\)
🔗
🔗
Answer 2.
\(\infty \)
🔗
🔗
Answer 3.
\(\infty \)
🔗
🔗
🔗

17.

For \(f(x) = {\left(4-x\right)\mathopen{}\left(4x-2\right)\mathopen{}\left(x^{2}-4\right)}\text{,}\) determine the `x`-intercepts and the end behavior. Enter intercepts as a comma separated list of points.
🔗
Intercepts :
🔗
🔗
Inputting the function into the Desmos tool below may help investigate the function.
🔗
Answer 1.
\(\left(4,0\right), \left(0.5,0\right), \left(2,0\right), \left(-2,0\right)\)
🔗
🔗
Answer 2.
\(-\infty \)
🔗
🔗
Answer 3.
\(-\infty \)
🔗
🔗
🔗

18.

For \(f(x) = {2x^{3}\mathopen{}\left(3x-5\right)}\text{,}\) determine the `x`-intercepts and the end behavior. Enter intercepts as a comma separated list of points.
🔗
Intercepts :
🔗
🔗
Inputting the function into the Desmos tool below may help investigate the function.
🔗
Answer 1.
\(\left(0,0\right), \left(1.66667,0\right)\)
🔗
🔗
Answer 2.
\(\infty \)
🔗
🔗
Answer 3.
\(\infty \)
🔗
🔗
🔗
🔗
PrevTopNext
Feedback