Question

practice and problem-solving exercises
practice
every year, the rock and roll hall of fame and museum inducts legendary musicians and musical acts to the hall. the table shows the number of inductees for each year.

1. represent the data using each of the following:

a. a mapping diagram
b. ordered pairs
c. a graph on the coordinate plane

1. what are the domain and range of this relation?

table: rock and roll hall of fame inductees
year: 2001, number of inductees: 11; 2002: 8; 2003: 9; 2004: 8; 2005: 7; 2006: 6
source: rock and roll hall of fame

determine whether each relation is a function.

1. mapping diagram: domain -9, 3, 5, 11; range -6, -2, 8, 21
2. mapping diagram: domain 3, 5, 6, 8; range -6, -2, 15, 21
3. mapping diagram: domain -14, -12, 1, 3; range -2, 15, 16, 21
4. {(3, -9), (11, 21), (121, 34), (34, 1), (23, 45)}

use the vertical-line test to determine whether each graph represents a function.

1. graph: a parabola opening to the right
2. graph: a parabola opening up
3. graph: a straight line with negative slope

evaluate each function for the given value of x, and write the input x and output f(x) as an ordered pair.

1. ( f(x) = 17x + 3 ) for ( x = 4 )
2. ( f(x) = -\frac{2x + 1}{3} ) for ( x = -5 )
3. ( f(x) = 2x - 33 ) for ( x = 9 )
4. ( f(x) = -9x - 2 ) for ( x = 7 )
5. ( f(x) = \frac{7}{3}x - 9 ) for ( x = 3 )
6. ( f(x) = -\frac{12x}{5} ) for ( x = -1 )
7. ( f(x) = 11x - 11 ) for ( x = -11 )
8. ( f(x) = \frac{2}{9}x - \frac{9}{2} ) for ( x = 9 )

write a function rule to model the cost per month of a long-distance cell phone calling plan. then evaluate the function for the given number of minutes.

1. monthly service fee: $4.52; rate: $.12 per minute; minutes used: 250
2. monthly service fee: $3.12; rate: $.18 per minute; minutes used: 175

Explanation:

Step1: Identify domain (years)

Domain: {2001,2002,2003,2004,2005,2006}

Step2: Identify range (inductees)

Range: {6,7,8,9,11}

Step1: Check x-values uniqueness

All x-values (3,11,121,34,23) are unique

Step2: Determine function status

Relation is a function

Step1: Substitute x=4 into f(x)

f(4)=17*4+3=68+3=71

Step2: Form ordered pair

(4,71)

Step1: Substitute x=-5 into f(x)

f(-5)=(-2*(-5)+1)/3=(10+1)/3=11/3

Step2: Form ordered pair

(-5, 11/3)

Step1: Substitute x=9 into f(x)

f(9)=2*9-33=18-33=-15

Step2: Form ordered pair

(9,-15)

Step1: Substitute x=7 into f(x)

f(7)=-9*7-2=-63-2=-65

Step2: Form ordered pair

(7,-65)

Step1: Substitute x=3 into f(x)

f(3)=(7/3)*3-9=7-9=-2

Step2: Form ordered pair

(3,-2)

Step1: Substitute x=-1 into f(x)

f(-1)=(-12*(-1))/5=12/5

Step2: Form ordered pair

(-1,12/5)

Step1: Substitute x=-11 into f(x)

f(-11)=11*(-11)-11=-121-11=-132

Step2: Form ordered pair

(-11,-132)

Step1: Substitute x=9 into f(x)

f(9)=(2/9)*9 -9/2=2-4.5=-5/2

Step2: Form ordered pair

(9,-5/2)

Step1: Define function rule

C(m)=4.52+0.12m

Step2: Evaluate for m=250

C(250)=4.52+0.12*250=34.52

Step1: Define function rule

C(m)=3.12+0.18m

Step2: Evaluate for m=175

C(175)=3.12+0.18*175=34.62

Answer:

1. Domain: {2001,2002,2003,2004,2005,2006}, Range: {6,7,8,9,11}
2. Yes, the relation is a function
3. (4, 71)
4. (-5, 11/3)
5. (9, -15)
6. (7, -65)
7. (3, -2)
8. (-1, 12/5)
9. (-11, -132)
10. (9, -5/2)
11. Function rule: C(m) = 4.52 + 0.12m, Cost for 250 minutes: $34.52
12. Function rule: C(m) = 3.12 + 0.18m, Cost for 175 minutes: $34.62