##### Notes

This printable supports Common Core Mathematics Standard HSF-IF.C.7, HSF-IF.C.7c

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# Graphing Polynomial Functions (Grades 11-12)

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## Graphing Polynomial Functions

Instructions: Ensure that all graphs are labeled correctly.

1.
When graphing a polynomial function of degree n, there will always be n distinct x-intercepts.
1. True
2. False
2.
When graphing a polynomial function of degree 8, whose leading coefficient is -3, which of the following is correct?
1. The function tends toward positive infinity as x approaches negative and positive infinity.
2. The function tends toward negative infinity as x approaches negative and positive infinity.
3. The function tends toward negative infinity as x approaches negative infinity, and the function tends toward positive infinity as x approaches positive infinity.
4. The function tends toward positive infinity as x approaches negative infinity, and the function tends toward negative infinity as x approaches positive infinity.
3.
Consider the polynomial function $P(x) = x^5 - x^4 - 93x^3 + 41x^2 + 1492x - 1440$ for the following questions.
A.
Using polynomial long division, find the resulting polynomial if -8 is a zero of the function.
1. $x^4 + 7x^3 - 37x^2 - 255x - 548$
2. $x^4 - 9x^3 -21x^2 +209x-180$
3. $x^4 - 9x^3 - 21x^2 - 127x + 2508$
4. $x^4 +7x^3 - 149x^2 + 1233x - 8354$
B.
Using the result from the previous question, and the fact that 9 is also a zero of the function $P(x)$, use polynomial division to find the result of $(P(x))/((x+8)*(x-9))$.
1. $x^3 - 18x^2 + 141x - 1060$
2. $x^3 - 18x^2 - 183x - 1438$
3. $x^3 - 21x + 20$
4. $x^2 - 8x + 43$
C.
What are the remaining zeros of the function P(x)?
1. -5, 1, and 4
2. There are no more zeros.
3. 1 and 4
4. -5 and 4
D.
What is the end behavior of P(x)? Select how the function P behaves as x approaches negative infinity and as x approaches positive infinity.
 $P -> -oo$ $P-> +oo$ $x -> -oo$ $x -> +oo$
E.
When graphing P(x), which of the following would be the best scale for the y-axis?
1. -10, -9, ..., 9, 10
2. -1,000, -900, ..., 900, 1,000
3. -5,000, -4,500, ..., 4,500, 5000
4. -10,000, -9,000, ...., 9,000, 10,000
F.
Graph the function $P(x)$.

4.
Graph: $y=2x^3-8x$

5.
Graph: $y=x(x+2)^2$

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