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Math 4R

RELATIONS & FUNCTIONS HOMEWORK

________HW # 6: Pg 3 WS – Domain ________HW # 7: 1. Text p. 105 - # 1-4 2. Find the domain and range:

(a) yx

x

2 1

2 (b) y

x

x2

1

(c) y x2 9 (d) y x 2 9

(e) yx

1

92 (Find the domain only)

________HW # 8: Pg 4 WS – More Domain and Range ________HW # 9: Pg 5 WS – Homework A7 ________HW # 10: Text – p. 93 - # 35 p. 94 - # 41, 42 p. 106 - # 45 ________HW # 11: 1. Pg 7-8 WS – Piecewise Functions - # 4 – 6 2. Study for Quiz on Types of Functions & Piecewise Functions

________HW # 12: Pg 9 WS – Transformations of Functions 1 Homework

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________HW # 13: Pg 10 WS – Transformations of Functions 2 Homework-#1 - 6

________HW # 14: Finish WS – Transformations of Functions 3 Classwork Study for Quiz on Transformations ________HW # 15: 1. Text p. 106 - # 29 – 34, 41, 43, 44

________HW # 16: 1. Suppose that xxf 2)( and 13)( 2 xxg .

Find:

(a) 4gf (b) 2fg

(c) 1ff (d) 0gg

2. Text pp. 128-9 - # 35 – 37, 47, 48, 67 ________HW # 17: Text pp. 128-9 - # 38, 49, 50, 61, 63, 66, 69 ________HW # 18: Text pp. 139-40 - # 1 – 4, 11 – 14, 61, 62 ________HW # 19: Pg 13 WS – Functions Review #1-7 STUDY FOR TEST !!!

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MATH 4R NAME___________________________ DOMAIN DATE___________________________ Find the domain of the functions below.

1. 81)( xxf 2. x

xxf

5)(

3

3. 1

3)(

xxf 4. 100)( 2 xxf

5. 7)( xxf 6. 9

67)(

2

3

x

xxxf

7. x

xxf

5100

2)(

8.

1)(

2

x

xxf

9. 16)( 2 xxf 10. 2

1)(

xxf

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MATH 4R NAME___________________________ MORE DOMAIN & RANGE DATE___________________________ Find the domain and range.

1. 5

1

xy 2.

xy

4

1

3. 2

3

xy 4.

1

5

x

xy

5. 1

4

xy 6.

2

2

x

xy

7. 5

x

xy 8.

2

23

x

xy

9. 32 xy 10. 1002 xy

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Homework A7 4R

1. For each of the following

a) Write the relation b) Find the domain c) Find the range d) State if it is a function

I. II.

2. Classify as polynomial, quadratic, linear, rational, or algebraic.

a) 2)( xxf b) )4(3)( xxf c) 4

2)(

2

x

xxg

d) )5)(3)(2()( xxxxf e) xxxh 2)( where , and are constants

3. Find the following. Write undefined if the function is not defined for a given value.

a) If 2

)(

x

xxf , find ).2(),1(),0( fff b) If xxxg 2)( , find )2(),2( gg

4. Find the domain of each of the following.

a) 42

4)(

x

xxf b) 43)( xxg c)

254

1)(

2

xxh

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MATH 4R NAME___________________________ PIECEWISE FUNCTIONS DATE___________________________ 1. The fine for speeding on a road with a speed limit of 45 kilometers per hour (kph) is $50; plus $5 for each kph from 46 to 55 kph; plus $10 for each kph from 56 to 65 kph; plus $20 for each kph from 66 kph and above. (a) Write a piecewise function to model the cost of the ticket. (b) Use your calculator to graph the piecewise function. (c) At what speed does the ticket exceed $250? 2.

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3. U.S. Travelers Abroad. The money C (in millions of dollars) spent by U.S. travelers in other countries increased in a linear pattern from 1980 to 1983. Then, in 1984, the money spent took a sharp jump and until 1988 increased in a different linear pattern. These two patterns can be approximated by the piecewise-defined function

,4.2350808,12

,1.917479,10

t

tC

84

30

t

t

where 0t represents 1980. Use this function to approximate the total amount spent by U.S.

travelers abroad between 1980 and 1988.

4. If

12

2)(

2

x

x

xf

0 if

0 if

0 if

x

x

x

, find: (a) f(-2)

(b) f(0) (c) f(2)

5. If

2

1)(

x

xxf

0 if

0 if

x

x , then:

(a) Find the domain of the function. (b) Graph the function by hand.

(c) Based on the graph, find the range.

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6. For the following function f ,

2

2

1

)(

x

x

xf

1 if

1 if

11- if

x

x

x

(a) Find f(0), f(1), and f(2). (b) Determine the domain of f .

(c) Graph f .

(d) Use the graph to find the range of f .

7. Cost of Electricity. In the winter, Commonwealth Edison Company supplies electricity to residences for a monthly customer charge of $8.91 plus 10.494 per kilowatt-hour (kWhr) for the first 400

kWhr supplied in the month, and 7.91 per kWhr for all usage over 400 kWhr in the month. (a) What is the charge for using 300 kWhr in a month? (b) What is the charge for using 700 kWhr in a month? (c) If C is the monthly charge for x kWhr, express C as a function of x .

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MATH 4R NAME___________________________ TRANSFORMATIONS OF FUNCTIONS 1 HOMEWORK DATE___________________________

Answer all questions for the given graph of )(xf . Carefully sketch )(xf after the given

transformation(s).

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MATH 4R NAME___________________________ TRANSFORMATIONS OF FUNCTIONS 2 HOMEWORK DATE___________________________

1. Consider the graph of the function )(xf 2. Consider the graph of the function

shown below. On the same set of axes, )(xf shown below. On the same

sketch the graph of the function set of axes, sketch the graph of the

1)3(2 xf function 2)1(21 xf .

3. Consider the graph of the function )(xf shown below. On the same set of axes,

sketch the graph of )(xf .

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4. Describe the transformations that the 5. Describe the transformations that the

graph of the function xxf )( graph of the function xxf )(

undergoes to produce the graph of the undergoes to produce the graph of

function 312)( xxg . the function 432)( xxg .

6. The graph of the function 2)( xxf was 7. The graph of the function xxf )(

transformed into the function )(xg whose was transformed into the function

graph is shown below. Determine the )(xg whose graph is shown below.

equation for the function )(xg . Determine the equation for the

function )(xg .

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MATH 4R NAME___________________________ FUNCTIONS REVIEW DO NOW DATE___________________________ For # 1 – 3, determine whether the given function is even, odd or neither.

1. xxxf 4)( 3 2. 31)( xxxg 3.

21)( xxxh

4. Graph

1

3

1

)(

x

x

xg

3x1 if

1 if

1 if

x

x

.

For # 5 – 8, find the domain of each function.

5. 9

)(2

x

xxf 6. xxf 2)(

7. x

xxh )( 8.

32)(

2

xx

xxf

9. Find the range of 5

2

x

xy .

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Math 4R Name___________________________ Functions Review Homework #17 Date_______________Period________ 1.

Input Value 10 5 0 5 10

Output Value -5 -2 1 2 5

a) The table above defines a relation. List the set of ordered pairs in the relation. ______________________________________________ b) List the set of elements in the domain. ______________________________________________ c) List the set of elements in the range. ______________________________________________ d) Is the relation a function? Yes or No, and explain why. ______________________________________________ 2. Evaluate the function at the specified values.

𝑔(𝑥) = {1

2𝑥 + 1, 𝑥 ≤ 2

𝑥 − 2, 𝑥 > 2 a)𝑔(−2) = b) 𝑔(2) = c)𝑔(10) =

3. Find the domain of the following functions.

a) 𝑓(𝑥) = √25 − 𝑥2 b) 𝑓(𝑥) = 3𝑥 + 4

c) 𝑔(𝑠) =5

3𝑠−9 d) 𝑓(𝑥) = √𝑥2 + 8𝑥

e) ℎ(𝑥) =𝑥

𝑥2−𝑥−6 f) ℎ(𝑡) = |𝑡 + 1|

4. Identify the transformation to the graph of the function 𝑓(𝑥) = √𝑥

a) ℎ(𝑥) = −√𝑥 ________________________________________

b) ℎ(𝑥) = √𝑥 + 3 ________________________________________

c) ℎ(𝑥) = √−𝑥 + 3 ________________________________________

d) ℎ(𝑥) = 2√𝑥 − 3 − 1______________________________________

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5. Determine the transformation of the graph of 𝑓(𝑥) = √𝑥 in the graphs below.

a) b)

c) d)

a)_______________b)_______________c)_______________d)_______________

6. Find 𝑓−1(𝑥) for the following functions.

a) 𝑓(𝑥) =1

2𝑥 − 3 b) 𝑓(𝑥) = 5𝑥 − 7

c) 𝑓(𝑥) = √𝑥 + 1 d) 𝑓(𝑥) = 𝑥3 + 2

7. Given the functions 𝑓(𝑥) = 5𝑥 − 7 and 𝑔(𝑥) = 2𝑥2 + 2, find each of the following: a) 𝑓(𝑔(3)) = b) 𝑔(𝑓(−2)) = c) 𝑓(𝑔(𝑥)) = d) 𝑔(𝑓(𝑥)) =