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

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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

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.

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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: _____________________________________________

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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. ____________________

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

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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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