# Function Worksheet - Page 8

Function Worksheet
• Page 8
71.
Jim's family required scuba equipment when they were on a vacation. The rent for the equipment was about $120 per day. Which of the following rules represents the relationship between the number of days rented and the rent to be paid?  a. Rent to be paid =$120 - Number of days rented b. Rent to be paid = $120 + Number of days rented c. Rent to be paid = d. Rent to be paid =$120 × Number of days rented

#### Solution:

The rent for the scuba equipment for 1 day is $120. As the number of days increases by 1, the rent to be paid increases by 120. So, the rule representing the relationship between the number of days rented and the rent to be paid can be given as, Rent to be paid =$120 × Number of days rented.

72.
The distance $d$ (in miles) that the sound travels in time $t$ seconds is represented by the rule $d$ = 0.2 $t$. Which of the tables satisfies the relationship for $t$ = 0, 5, 10 and 15?

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

d = 0.2 t
[Original expression.]

0.2 × 0 = 0 miles
[The distance traveled in 0 seconds.]

0.2 × 5 = 1 mile
[The distance traveled in 5 seconds.]

0.2 × 10 = 2 miles
[The distance traveled in 10 seconds.]

0.2 × 15 = 3 miles
[The distance traveled in 15 seconds.]

The distance traveled in 0, 5, 10, 15 seconds is 0, 1, 2 and 3 miles.

These values are represented as shown in Table 2.

So, Table 2 satisfies the relationship by substituting the values of t.

73.
Hardy earns $9 per hour. Which of the following rules describes the relation between the number of hours he worked and the amount he earns?  a. Earnings =$9 + number of hours b. Earnings = $9 - number of hours c. Earnings =$9 / number of hours d. Earnings = $9 x number of hours #### Solution: As the number of working hours increase the amount he earns also increases at the rate of$9 / hr.

So, the number of hours he worked and the amount he earns is given by the relation,
Earnings = $9 x number of hours. Correct answer : (4) 74. Which of the following function rules satisfies the table?  a. $f$ ($n$) = 2$n$ + 1 b. $f$ ($n$) = 2$n$ - 1 c. $f$ ($n$) = 2$n$ d. $f$ ($n$) = 2$n$ + 2 #### Solution: A function is an entity, which gives the relationship between the output and input. The function is denoted by f(n). Let n represent the input in the table. Output = 2 × Input + 1 = 2 × n + 1 The function, which satisfies the table is f(n) = 2n + 1. Correct answer : (1) 75. A club charges$24 per head as membership fee. If 13 people become the members, then what is the amount collected?
 a. $352 b.$332 c. $292 d.$312

#### Solution:

Let n represent the membership fee for 13 members.

f(n) = $24 × n [Original expression.]$24 × 13 = $312 [Calculate the membership fee for 13 people.] The amount collected is$312.

76.
Which of the tables describes the function $f$($n$) = - 4$n$ + 6 if $n$ = 0, 1, 2, 4?

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

f(n) = - 4n + 6
[Original function.]

f(0) = - 4(0) + 6 = 6
[Substitute n =0.]

f(1) = - 4(1) + 6 = 2
[Substitute n = 1.]

f(2) = - 4(2) + 6 = - 2
[Substitute n = 2.]

f(4) = - 4(4) + 6 = - 10
[Substitute n = 4.]

The values obtained can be shown in the form of a table as shown in Table 4.

So, Table 4 is the table describing the function.

77.
Which of the tables gives the input - output relationship for the rule $y$ = 5$x$ + 2 where $x$ = 1, 2, 3, 4?

 a. Table 1 b. Table 2 c. Table 3 d. Table 4

#### Solution:

y = 5x + 2
[Original equation.]

y = 5(1) + 2 = 7
[Substitute x = 1.]

y = 5(2) + 2 = 12
[Substitute x = 2.]

y = 5(3) + 2 = 17
[Substitute x = 3.]

y = 5(4) + 2 = 22
[Substitute x = 4.]

The values obtained can be shown in the form of a table as shown in Table 2.

So, Table 2 gives the input-output relationship for the rule.

78.
Which of the following rules describes the input-output value in the table?

 a. $f$ ($x$) = $x$ + 6 b. $f$ ($x$) = 2$x$ - 5 c. $f$ ($x$) = 2$x$ + 7 d. None of the above

#### Solution:

The values of f(x) obtained when x = -3, 0, 3, 6 in f(x) = x + 6 are 3, 6, 9 and 12.

The values of f(x) obtained when x = -3, 0, 3, 6 in f(x) = 2x + 7 are 1, 7, 13 and 19.

The values of f(x) obtained when x = -3, 0, 3, 6 in f(x) = 2x - 5 are -11, -5, 1 and 7.

The values of f(x) obtained when x = -3, 0, 3, 6 in f(x) = 2x - 7 are -13, -7, -1 and 5.

The values of f(x) obtained for the function f(x) = 2x + 7 are same as that of the values shown in the table.

So, f(x) = 2x + 7 is the function rule describing the input-output values in the table.

79.
A soap manufacturing company packs the soaps in cartons. Which of the following rules represents the relationship between the cartons and soaps, if 109 soaps are packed in one carton?
 a. Number of soaps = 109 / Number of cartons b. Number of soaps = 109 × Number of cartons c. Number of soaps = 109 + Number of cartons d. Number of soaps = 109 - Number of cartons

#### Solution:

Number of soaps that fit in 1 carton = 109

As the number of cartons increase by 1, the number of soaps increase by 109.

So, the rule representing the relationship between the soaps and the cartons can be given as, Number of soaps = 109 × Number of cartons.