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Analyzing Functions

For 1–5, use the graph of the quadratic function [pic]

1. Write the domain of the function as an inequality, using

set notation and interval notation.

2. Write the range of the function as an inequality, using

set notation and interval notation.

3. Describe the end behavior of the function.

4. What are the zeros of the function?

5. What is the range of the function if the domain is restricted to [pic]

6. A student reads 3 pages of a book every 5 minutes for 1 hour. Write a function that models this situation. Determine a domain from the situation and identify the range. Use interval notation for the domain and range.

7. The graph shows a function that models the number N of seniors from a high school accepted at a four-year university as a function of time t in years over a

ten-year period.

Is the function increasing on each of the following intervals?

A [pic] [pic] Yes [pic] No

B [pic] [pic] Yes [pic] No

C [pic] [pic] Yes [pic] No

8. The table shows some values of a polynomial function.

|x |0 |1 |2 |3 |4 |

|g(x) |80 |100 |60 |20 |40 |

Find the average rate of change of the function over each of the following intervals? On which of the following intervals would it appear that the function is increasing?

A From [pic]

B From [pic]

C From [pic]

D From [pic]

Absolute Value Functions, Equations, and Inequalities

Use the graph below for 1–4.

1. Write a function in standard form to match the graph. Let b ’ 1.

2. Find the vertex of the function.

3. Find the domain of the function.

4. Find the range of the function.

5. Given that [pic] determine if each statement is True or False.

A The domain is all real numbers.

[pic] True [pic] False

B The vertex is (0, −3).

[pic] True [pic] False

C The vertex is (0, 3).

[pic] True [pic] False

D The range is all real numbers.

[pic] True [pic] False

6. If [pic] write a function h(x) that is g(x) translated down 2 units.

7. Graph [pic]

8. Determine any solutions to [pic]

9. Is each equation’s graph entirely in quadrant III and IV?

A [pic] [pic] Yes [pic] No

B [pic] [pic] Yes [pic] No

10. Solve [pic]

11. Solve [pic]. Graph solutions on a number line.

12. Graph [pic]

13. Graph the solutions to [pic]

[pic]

14. A company ordered 5-foot long steel rods. The length of the rods that the company received vary from a maximum length of 0.05 inches longer than 5 feet to a minimum length of 0.05 inches shorter than 5 feet. Write and solve an absolute value inequality to represent the possible length of each rod in inches.

For 16–17, solve the absolute equation or inequality graphically.

15. [pic]

16. [pic]

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