Algebra II - Transformation Retest Review



PreCal Unit 1 review Name: Period:

1) Write the description of each transformation, draw the graph and write the domain and range of the function.

1) [pic] 2) [pic] 3) [pic]

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D: ___________________ D:____________________ D: __________________

R: ___________________ R:____________________ R: ___________________

[pic] [pic] [pic]

4) 5) [pic] 5) [pic] 6)[pic]

______________________ ______________________ _____________________

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D: ___________________ D:____________________ D: __________________

R: ___________________ R:____________________ R: ___________________

[pic] [pic] [pic]

2) Write the equation of each parent function given the certain conditions.

• 11) Absolute Value: Vertical Compression of [pic], shifted up 4 units, shifted left 3 units. _______________

• 12) Cubic: Shifted 3 down, shifted 1 left, and reflected across the x-axis. _______________

• 13) Quadratic: Reflected across x-axis, Vertical stretch of 3, shifted down 2. _______________

• 14) Rational: Shifted 6 right, 7 up ______________

3) Use the graph to answer the questions:

|1.) Is f increasing on the interval [pic] ? |

|2.) Is f increasing on the interval [pic] ? |

|3.) List the interval(s) on which f is increasing. |

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|4.) Is there a local maximum at 2? |

|If yes, what is it? |

|5.) List the numbers at which f has a local maximum. |

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|What are the local maximums? |

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|6.) Find the x- and y-intercepts, if any. |7.) State the domain and range. |

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| 8.) State the intervals on which it is increasing, |9.) Is the function even, odd, or neither? |

|decreasing, or constant. | |

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4) Determine algebraically whether each function is even, odd, or neither.

| [pic] | [pic] | [pic] |

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5 ) Determine whether each function is even, odd, or neither.

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6 ) Carefully graph each of the following. Then evaluate the function at the specific value.

[pic] [pic]

[pic]

[pic]

7 ) Write the equation of the piece wise graph :

8) Perform the indicated operations.

1. [pic] 2.[pic]

3. [pic] 4. [pic]

5. [pic] 6. [pic]

9) Factor completely.

7. [pic] 8. [pic]

9. [pic] 10. [pic]

10) Find the quotient and remainder using long division:

A. [pic]

B. [pic]

11) Find the remainder using synthetic division :

A. [pic]

B. [pic]

12. Write an equation with degree of 3 whose zeros are 4 and -2.

13. Find the degree of each of the polynomials:

A. y = -3x7 + x5 - 3x2 + 2 B. y = 2x(x-4)2(x+2)3(x-3)4

14. Sketch a graph of the following functions. Label all zeros.

A. P(x) = x5 - 9x3 B. P(x) = -2(x-1)(x-2)2(x+1)3

15. List the end behavior of the following polynomials:

A. Q(x) = -x2(x2 – 4) As [pic], [pic] As[pic], [pic]

B. S(x) = [pic]x6 – 2x4 As [pic], [pic] As[pic], [pic]

C. P(x) = x4 – 3x2 - 4 As [pic], [pic] As[pic], [pic]

16. Use the following graph

[pic]

A. Find the end behavior of the graph

As [pic], [pic] As[pic], [pic]

B. List the zeros of the graph

C. List the local extrema of the graph. Label each as a local min or max

D. List the interval(s) where the graph is increasing

E. List the interval(s) where the graph is decreasing

17. CALCULATOR ALLOWED: Find the relative extrema of the following functions and list all the interval(s) in which the graph is increasing or decreasing. Round to three decimals.

A. f(x) = x4 – 3x3 – 3x2 + x – 2 B. f(x) = -x3 – 4x2 - x + 3

18- What is the end behavior of these graphs?

[pic]

[pic]

[pic]

[pic]

19) Fill the blanks about this graph :

Vertical asymptote:

Horizontal asymptote:

[pic]

[pic]

[pic]

[pic]

Increasing:

Decreasing:

20) Find the domain and range and state if this function is increasing or decreasing?

[pic] [pic]

Domain: Domain:

Range: Range:

Increasing or Decreasing? Increasing or Decreasing?

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[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

[pic]

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