Honors Precalculus Worksheet Polynomial Functions No ...

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Honors Precalculus Worksheet Polynomial Functions No ...

Honors Precalculus Worksheet

Polynomial Functions

No Calculators Allowed

4 3 2

Given P( x) = 6x + 13x − 34x − 47x

+ 30

1. List all possible rational zeros.

2. Find the y-intercept

3. What is the maximum number of turning points

4. How many zeros does P(x) have

5. Use limit notation to describe the end behavior of the graph P(x).

6. What does Descartes Rule of Signs tell you about the zeros

7. If

5

− and 2 are zeros of P(x), find the other zeros.

3

8. Write P(x) in factored form. 9. Graph P(x)


Precalculus/Trig Homework

Properties of graphs of functions

Name_______________________

Use your calculator to graph each function (save the document) and find the open intervals on which the

function is increasing, decreasing, concave up, and concave down. Find and label on the graph any

relative extrema and inflection points, and use limit notation to describe the end behavior.

1.

f x x x

3 2

( ) = − 2 + 6 − 3

a) increasing________________________

b) decreasing _______________________

c) relative max(s) is _______ at x = ______

d) relative min(s) is _______ at x = ______

e) concave up _______________________

f) concave down _____________________

g) inflection point(s) __________________

h) end behavior ______________________

2.

g x x x

4 3

( ) = − 4 + 1

a) increasing________________________

b) decreasing _______________________

c) relative max(s) is _______ at x = ______

d) relative min(s) is _______ at x = ______

e) concave up _______________________

f) concave down _____________________

g) inflection point(s) __________________

h) end behavior ______________________


x

3. h( x)

=

2

x + 1

a) increasing________________________

b) decreasing _______________________

c) relative max(s) is _______ at x = ______

d) relative min(s) is _______ at x = ______

e) concave up _______________________

f) concave down _____________________

g) inflection point(s) __________________

h) end behavior ______________________

2

4. k( x) = e x

( x − 3)

a) increasing________________________

b) decreasing _______________________

c) relative max(s) is ________ at x = ______

d) relative min(s) is ________ at x = ______

e) concave up _______________________

f) concave down _____________________

g) inflection point(s) __________________

h) end behavior ______________________

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