Unit 1 Review PreCalc

Name: ____________________________________________________________

S1

Unit 1 - Functions Analysis

PC

Test Review

Instructions: All answers must be accompanied with valid mathematical justification (show your work) to receive

credit. All answer should be EXACT, unless otherwise noted.

1. Graph | 4 5 . Then state the inequality in INTERVAL notation. (NON-CALCULATOR)

2. Find the domain of 28 7 . Write your answer in set builder notation. (NON-CALCULATOR)

3. Find the domain of the function. Write it in Interval notation. (NON-CALCULATOR)

4 16 3 27

4. Identify the domain and range for the graph below:

Domain: Range:

5. ALGEBRAICALLY, determine the symmetry of the following equation with respect to the origin, y-axis, x-axis, and line y=x. YOU MUST SHOW YOUR WORK FOR CREDIT. Clearly state or circle which symmetry exists for the equation. (NON-CALCULATOR)

18 7 2

6. Is

1 Odd, Even, Both or Neither?

EXPLAIN how you got your results in full and complete sentences and show all work.

7. Analyze the following function. Provide all the information listed below. Round to the nearest hundredth if needed. 2 5 6

End Behavior: , ,

Extrema (Maxs/Mins). Circle RELATIVE or ABSOLUTE as appropriate RELATIVE or ABSOLUTE Maximum @ RELATIVE or ABSOLUTE Minimum @

 2 5 6

Intervals of Increasing/Decreasing - Interval notation only

X-intercepts

Increasing:

Decreasing:

Y-intercepts

For #8 ? 9, choose 2 of the following to graph. Indicate your choice for each graph by writing the equation next to the graph. Use and label at least three points, it may be necessary to use more to draw an accurate graph. No table is needed. (NON-CALCULATOR)

Choices:

| 4| 1

2 2 3

2 2

5

1 2

8. Equation: _______________________________

y 10

8 6 4 2

?10 ?8 ?6 ?4 ?2 ?2 ?4 ?6 ?8

?10

2 4 6 8 10 x

9. Equation: ___________________________________

y 10

8 6 4 2

?10 ?8 ?6 ?4 ?2 ?2 ?4 ?6 ?8

?10

2 4 6 8 10 x

10. Write an exact equation for the absolute value function that represents the graph at left:

11. Graph the piece-wise function:

9 2

1 2 4

3 7 4 10

y 10

8 6 4 2

?10 ?8 ?6 ?4 ?2 ?2 ?4 ?6 ?8

?10

2 4 6 8 10 x

12. Write the piecewise function that represents the graph at right:

13. Know how to ACCURATELY complete the graph below given that the function is even or odd.

EVEN

ODD

14. If indicated.

A.)

1,

2 3

1 4 , Find the following new functions as well as any values B.) 4

B.) 3

D.)

15. Find and verify the inverse of . Then state the domain and range of the inverse, using interval notation. YOU MUST SHOW YOUR WORK FOR VERIFYING BELOW.

3 2 4

Verifying work:

Domain: Range:

OR

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