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Date: ___________________
Per: ________
Algebra 2H
Polynomial Functions Review
(sections 5.3, 5.4, 5.7, even/odd)
1. Given f(x) = 3x5 + 2x4 – 3x3 – 6x2, answer the
following about its graph.
2. Given the graph of g(x), answer the following.
a) Describe the end behavior.
b) What is the maximum number of turning points?
c) Does the graph have extrema?
d) Find f(–2).
a) What is the least possible degree of g(x)?
b) Identify the extrema, if it exists.
c) How many real zeros does g(x) have?
d) What is the range?
3. Find all the zeros of f(x)= x4 – 6x3 + 9x2 + 6x – 10
4. Given f(3) = 0, find all the zeros of
f(x) = x3 + 3x2 – 34x + 48.
5. Write a polynomial function of least degree that
has real coefficients, a leading coefficient of 1, and
zeros 5, 5, and –7i.
6. Write a polynomial function of least degree that
has real coefficients, a leading coefficient of 1, and
zeros 6 and –1 – i.
For #7-8, sketch the polynomial function without using a calculator. Label intervals on the axes.
7. f(x) = (x – 3)3(x + 2)
8. A function that has:
 degree 3
 a negative leading coefficient
 root of x = 2
 double root of x = –4
9. You want to make a rectangular box that is x cm high, (x + 6) cm long, and (12 – x) cm wide. What is the greatest
volume possible? What will be the dimensions of the box for this volume? Round to the nearest hundredth.
10. The demand function for a type of phone is given by the model p = 100 – 8x2 where p is the price per phone in
dollars and x is the number of phones produced in millions. The production cost is $25 per phone. The
production of 2.5 million phones yielded a profit of $62.5 million. What other number of phones could the
company sell to make the same profit? Round to the nearest thousand.
11. Verify that two zeros of the function f(x) = x4 – 4x3 – x2 – 16x – 20 are 2i and 5. Then state how many imaginary
and how may real zeros it has.
12. Which functions have the end behavior as x  –∞, f(x)  –∞ and as x  +∞, f(x)  +∞? Check all that apply.
 f(x) = 2x5 + x4 + x – 9
 f(x) = x3 – 7x2 + x – 3
 f(x) = x4 – 3x2 + 2x
 f(x) = 6x + 1
 f(x) = x6 – 3x2 + 2
 f(x) = 6x4 + 2x3
13. Which function(s) are even? Check all that apply.
 f(x) = x4 + 2x2
 f(x) = x3 + x – 4
14. The graph of a polynomial function is shown to the right. Which of the following
could be the degree of the function? Check all that apply.
 5
 3
 4
 6
15. Consider a polynomial function in standard form. Hannah claims that if every non-constant term has an even
exponent, the function is even. She also claims that if every non-constant term has an odd exponent, the
function is odd. Are each of her claims correct?
16. Draw a cubic function with a negative leading coefficient that is also an odd function.