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Lesson 3.1 and 3.2 Graphing and Analyzing Graphs of Polynomial Functions

Last updated over 1 year ago

12 questions

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Lesson 3.1 Graph Polynomial Functions

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Lesson 3.2 Analyze Graphs of Polynomial Functions

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Question 1

1.

What were the main mathematical concepts covered in class?

Question 2

2.

Describe how the graph of

is related to

Then graph f(x) and g(x) on the same coordinate plane. Use a table and label three points for each graph.

Question 3

3.

Describe how the graph of

is related to

Then graph f(x) and g(x) on the same coordinate plane. Use a table and label three points for each graph.

Question 4

4.

A general equation for the polynomial function g(x) is given along with the function’s graph. Use the reference points shown on each graph to identify values of the parameters and write a specific equation for the graphed function.

Question 5

5.

A general equation for the polynomial function g(x) is given along with the function’s graph. Use the reference points shown on each graph to identify values of the parameters and write a specific equation for the graphed function.

Question 6

6.

Use a graphing calculator to graph the polynomial function. Determine the x-intercepts, whether the graph crosses or is tangent to the x-axis at the x-intercept, the number of turning points, and the number and type (global, or local but not global) of any maximum or minimum values.

Question 7

7.

Use a graphing calculator to graph the polynomial function. Determine the x-intercepts, whether the graph crosses or is tangent to the x-axis at the x-intercept, the number of turning points, and the number and type (global, or local but not global) of any maximum or minimum values.

Question 8

8.

Ricardo is creating an open-top box from a piece of cardboard. He forms a square flap of side length x at each corner by making a single cut (solid line) and then folding (dashed line) to form the flap. He then folds up the four sides of the box and glues each flap to the side it overlaps. What value of x, to the nearest tenth, maximizes the box’s volume.

Question 9

9.

Sketch a graph of the polynomial function.

Question 10

10.

Sketch a graph of the polynomial function.

Question 11

11.

Write a cubic or quartic function with the least degree possible in intercept form for the given graph. Assume that all x-intercepts are integers, and that the constant factor a is either 1 or -1.

Question 12

12.

Write a cubic or quartic function with the least degree possible in intercept form for the given graph. Assume that all x-intercepts are integers, and that the constant factor a is either 1 or -1.