the parent functions - ms. 6 module 1 ¢â‚¬â€œ polynomial,...

Download THE PARENT FUNCTIONS - Ms. 6 Module 1 ¢â‚¬â€œ Polynomial, Rational, and Radical Relationships Parent Function

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  • 1

    Module 1 – Polynomial, Rational, and Radical Relationships

    THE PARENT FUNCTIONS

    LINEAR ABSOLUTE VALUE

    y = x y = |x|

    EXPONENTIAL CUBE ROOT

    y =2X, b > 0 3y x

    QUADRATIC SQUARE ROOT

    y = x2 y = x

  • 2

    Module 1 – Polynomial, Rational, and Radical Relationships

    For the graphs given below answer the questions given.

    1. a. What type of function is given on the right?

    b. What is the equation of the function?

    2. a. What type of function is given on the right?

    b. What is the equation of the function?

    c. What is the x-intercept?

    d. What is the y-intercept?

  • 3

    Module 1 – Polynomial, Rational, and Radical Relationships

    3. a. What type of function is given on the right?

    b. What is the equation of the function?

    4. a. Describe what happened to the parent

    function for the graph at the right.

    b. What is the equation of the function?

    c. Write the equation in standard form.

    d. What is the importance of the x-intercept in graph?

    e. How many zeros of the function are there in this graph?

  • 4

    Module 1 – Polynomial, Rational, and Radical Relationships

    5. a. Describe what happened to the parent

    function for the graph at the right.

    b. What is the equation of the function?

    c. Write the equation in standard form.

    d. What is the importance of the x-intercept in graph?

    e. How many zeros of the function are there in this graph?

    6. a. Describe what happened to the parent

    function for the graph at the right.

    b. What is the equation of the function?

    c. Write the equation in standard form.

  • 5

    Module 1 – Polynomial, Rational, and Radical Relationships

    7. a. Describe what happened to the parent

    function for the graph at the right.

    b. What is the equation of the function?

    c. Write the equation in standard form.

    8. a. Describe what happened to the parent

    function for the graph at the right.

    b. What is the equation of the function?

    c. Write the equation in standard form.

  • 6

    Module 1 – Polynomial, Rational, and Radical Relationships

    Parent Function Worksheet # 1- 7 Give the name of the parent function and describe the transformation represented. 1. g(x) = x 2 – 1 Name: ______________________________________

    Transformation: ________________________________

    2. f(x) = 2 1x Name: ______________________________________

    Transformation: ________________________________

    3. h(x) = 2x Name: ______________________________________

    Transformation: ________________________________

    4. g(x) = x2+ 3 Name: ______________________________________

    Transformation: ________________________________

    5. g(x) = -3x Name: ______________________________________

    Transformation: ________________________________

    6. f(x) = 5x  - 2 Name: ______________________________________

    Transformation: ________________________________ 7. h(x) = x+6 Name: ______________________________________

    Transformation: ________________________________ #8-12 Identify the domain and range of the function. Describe the transformation from its

    parent function.

    8. g(x) = 3 x Domain : _____________________ Range : ___________________

    Transformation: _____________________________________________ 9. h(x) = - x2 + 1 Domain : _____________________ Range : ___________________

    Transformation: _____________________________________________

  • 7

    Module 1 – Polynomial, Rational, and Radical Relationships

    10. h(x) = 2x  Domain : _____________________ Range : ___________________

    Transformation: _____________________________________________

    11. f(x) = 3

    4 x Domain : _____________________ Range : ___________________

    Transformation: _____________________________________________ 12. h(x) = 6 (x + 9) 2 Domain : _____________________ Range : ___________________

    Transformation: _____________________________________________

    #13 - 17 Given the parent function and a description of the transformation, write the

    equation of the transformed function, f(x). 13. Absolute value—vertical shift up 5, horizontal shift right 3. ____________________

    14. Radical—vertical compression by 2

    5 ____________________

    15. Quadratic—reflected over the x axis and vertical shift down 2 ____________________

    16. Linear—vertical stretch by 8 ____________________

    17. Quadratic—vertical compression by .45, horizontal shift left 8. ____________________

    18. Which graph best represents the function f(x) = 2x2 - 2? ________________

    a. b. c. d.

  • 8

    Module 1 – Polynomial, Rational, and Radical Relationships

    What type of relationship is indicated by the given set of ordered pairs? How do you know? Explain or show your reasoning.

    X Y

    0 -2

    1 1

    2 4

    3 7

    4 10

    5 13

    x ax+b First

    Difference

    0

    1

    2

    3

    4

    5

  • 9

    Module 1 – Polynomial, Rational, and Radical Relationships

    What type of relationship is indicated by the given set of ordered pairs?

    X Y First Difference Second Difference

    0 -2

    1 0

    2 4

    3 10

    4 18

    5 28

    x ax 2 +bx+c

    First Difference

    Second Difference

    0

    1

    2

    3

    4

    5

  • 10

    Module 1 – Polynomial, Rational, and Radical Relationships

    1. Create a table to find the second differences for the polynomial 16 – 4t2 for integer

    values of t from 0 to 5.

    x  216 t First

    Difference Second

    Difference

    0

    1

    2

    3

    4

    5

    2. Show that the set of ordered pairs (x, y) in the table below satisfies a linear relationship.

    Find the equation of the form y = ax + b that all of the ordered pairs satisfy.

    X Y First Difference

    0 4

    1 1

    2 -2

    3 -5

    4 -8

    5 -11

  • 11

    Module 1 – Polynomial, Rational, and Radical Relationships

    3. Show that the set of ordered pairs (x, y) in the table below satisfies a quadratic

    relationship. Find the equation of the form y = ax2 + bx + c that all of the ordered pairs satisfy.

    X Y First Difference Second Difference

    0 1

    1 2

    2 -1

    3 -8

    4 -19

    5 -34

    4. (a) What type of relationship is indicated by the following set of ordered pairs?

    X Y

    0 0

    1 1

    2 6

    3 15

    4 28

    5 45

    (b) Find the equation that all ordered pairs above satisfy.

  • 12

    Module 1 – Polynomial, Rational, and Radical Relationships

    For each problem answer the following questions:

    a. What type of relationship is indicated by the following set of ordered pairs?

    b. Find an equation that all ordered pairs satisfies.

    1.

    X Y

    0 36

    1 20

    2 -28

    3 -108

    4 -220

    5 -364

    2.

    X Y

    0 5

    1 4

    2 -1

    3 -10

    4 -23

    5 -40

    3.

    X Y

    0 0

    1 2

    2 10

    3 24

    4 44

  • 13

    Module 1 – Polynomial, Rational, and Radical Relationships

  • 14

    Module 1 – Polynomial, Rational, and Radical Relationships

    Multiply and combine like terms to write as the sum or difference of monomials. 1. (g + 5) + (2g + 7) 2. (5d + 5) – (d + 1) 3. ( – 3x – 3) + (2 + 7x – 2) 4. (–2 – 3f – 5) + (–2 – 3f + 8) 5. –5(2 – ) 6. (2x + 9) 7. 8. (2x – 3)(3x – 5) 9. (r – 2t)(r + 2t) 10. (3y + 4)(2y – 3) 11. (3 – 2b)(3 + 2b) 12. 13. (3 + 1) + (8 – 8) 14. (6w – 11 ) – (4 + 7 ) 15. (w + 2t)( – 2wt + 4 ) 16. (x + y)( – 3xy + 2 )

    17. 18.

    19. 20.

    21. 22.

    23. 24.

    25. 26.

    27. (𝑥+2)(𝑥+2)(𝑥+2) 28.

    29. 29.

    30

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