1) Relate the end behavior to the domain and range of a polynomial function. How can knowing one give you information about the other?
For problems 2-4, determine of the statement is always, sometimes, or never true. Explain your answers.
2) A cubic function has \(3\) x-intercepts.
3) A quartic function has range \((-\infty,\infty)\).
4) A polynomial function with even degree has an end behavior:
“As \(x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ +\infty,\ \text{as}\ \ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ +\infty\)”.
For problems 5-7, match the graph with the correct function given below:
A) \(f(x)=-3x^3+12x-2\) B) \(g(x)=3x^4-10x^3+8x^2-1\) C) \(h(x)=3x^5-6x^2+2\)
5) 6) 7)
For problems 2-4, determine of the statement is always, sometimes, or never true. Explain your answers.
2) A cubic function has \(3\) x-intercepts.
3) A quartic function has range \((-\infty,\infty)\).
4) A polynomial function with even degree has an end behavior:
“As \(x\ \longrightarrow\ -\infty,\ f(x)\ \longrightarrow\ +\infty,\ \text{as}\ \ x\ \longrightarrow\ +\infty,\ f(x)\ \longrightarrow\ +\infty\)”.
For problems 5-7, match the graph with the correct function given below:
A) \(f(x)=-3x^3+12x-2\) B) \(g(x)=3x^4-10x^3+8x^2-1\) C) \(h(x)=3x^5-6x^2+2\)
5) 6) 7)
|
|
|
For problems 8-11, determine the least degree of the polynomial shown and the sign of the leading coefficient.
8)
9)
10)
11)
For problems 12-14, determine the end behavior of the polynomial without graphing.
12) \(f(x)=-3x^3-5x^2+x-1\)
13) \(f(x)=7x^6-3x^4+x^2\)
14) \(f(x)=2x^5-8x^4+x^3+7\)
For problems 15-16, identify the degree, leading coefficient, end behavior, and x- and y-intercepts. Then use this information to sketch a graph of the polynomial.
15) \(g(x)=-\frac{1}{2}(x-3)^2(x-1)(x+2)\)
16) \(h(x)=(x+1)^2(x-4)^2(x-2)^2\)
17) Use a graphing device to analyze the polynomial function \(f(x)=2x^4+11x^3+16x^2-4\). Be sure to identify the following:
- The degree
- The end behavior
- The x-intercepts and their multiplicity
- The y-intercept
- The maxima and minima
- The domain and range
Solution Bank