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Function Worksheet - Page 5

Function Worksheet
  • Page 5
 41.  
Tom bought a belt for $1.50. Which graph shows the relationship between the number of belts and the total cost of them?

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


Solution:

Cost of one belt = $1.50.

Cost of two belts = 2 × $1.50 = $3.

Cost of three belts = 3 × $1.50 = $4.50.

Cost of four belts = 4 × $1.50 = $6.

Cost of five belts = 5 × $1.50 = $7.50.

Among the graphs, Graph 3 represents the exact relation between the number of belts and the total cost of them.


Correct answer : (2)
 42.  
Max wanted to buy a toy that costs $2. Which graph shows the relationship between the number of toys and the total cost?

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


Solution:

Cost of one toy = $2.

Cost of two toys = 2 × $2 = $4.

Cost of three toys = 3 × $2 = $6.

Cost of four toys = 4 × $2 = $8.

Similarly, the cost of 5, 6, 7 and 8 toys are $10, $12, $14, $16 respectively.

Among the graphs, Graph 1 represents the exact relation between the number of toys and the total cost of them.


Correct answer : (2)
 43.  
Which rule is used for y in the ordered pairs on the graph?

a.
x × 4
b.
x × 3
c.
x + 4
d.
2x × 4


Answer: (a)


Correct answer : (1)
 44.  
Charlie traveled 400 miles at 40 mhr and 200 miles at 20 mhr. How long did the trip take?
a.
10 hours
b.
40 hours
c.
20 hours
d.
60 hours


Solution:

Charlie traveled 400 miles at 40 mph.
[Given]

Time taken to cover 400 miles at 40 mph = 400 / 40 = 10 hours.

He traveled 200 miles at 20 mph.
[Given]

Time taken to cover 200 miles at 20 mph = 200 / 20 = 10 hours.

Total time taken for the entire trip = 10 + 10 = 20 hours.


Correct answer : (3)
 45.  
A taxi company's fares are displayed in the table. How much would Sally pay if she travels 8.3 miles?

a.
$24.90
b.
$49.80
c.
$2.49
d.
$249.00


Solution:

From the table it is observed that, miles × $3 = fare.

If Sally travels 8.3 miles, then 8.3 × $3 = $24.90.

S0, Sally would pay $24.90 if she travels 8.3 miles.


Correct answer : (1)
 46.  
The table shows the relationship between the rental charges of a car and the number of days hired.
Number of days1246
Car rental charges$45$90$180$270

If Mathew hires a car for 9 days, then how much amount will he need to pay?
a.
$225
b.
$405
c.
$255
d.
$425


Solution:

From the table it is observed that, the rental charge of a car for a day = $45.

So, the rule for the table is, rental charges = 45 × n, where n is the number of days.

If Mathew hires the car for 9 days, then the amount he will pay = $45 × 9 = $405.
[Substitute n = 9]


Correct answer : (2)
 47.  
Jim deposited $20 initially in his bank account. Then he deposited $15 every week. The total savings c = 20 + 15n, n represents the number of weeks he deposited money in the bank. Identify the table that best represents the equation.


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


Solution:

c = 20 + 15n
[Original equation.]

c = 20 + 15(0)
[Substitute 0 for n.]

= 20
[Simplify.]

c = 20 + 15(1)
[Substitute 1 for n.]

= 35
[Simplify.]

c = 20 + 15(2)
[Substitute 2 for n.]

c = 50
[Simplify.]

c = 20 + 15(3)
[Substitute 3 for n.]

c = 65
[Simplify.]

c = 20 + 15(4)
[Substitute 4 for n.]

= 80
[Simplify.]

c = 20 + 15(5)
[Substitute 5 for n.]

= 95
[Simplify.]

The input and output values of table-1 matches with the results of the equation.

Table 1 satisfies the equation.


Correct answer : (3)
 48.  
A taxi company's fares are displayed in the table. How much would Sally pay if she travels 8.3 miles?

a.
$49.80
b.
$2.49
c.
$249.00
d.
$24.90


Solution:

From the table it is observed that, miles × $3 = fare.

If Sally travels 8.3 miles, then 8.3 × $3 = $24.90.

S0, Sally would pay $24.90 if she travels 8.3 miles.


Correct answer : (4)
 49.  
Which of the following best describes the relationship between the hours and wages shown in the table?
Hours1234
Wages ($)8162432

a.
wages × 8 = number of hours
b.
wages + 8 = number of hours
c.
wages = 8 × number of hours
d.
wages = 8 + number of hours


Solution:

Wages for an hour is $8, for two hours = 2 × 8 = 16, for three hours = 3 × 8 = $24 and so on.
[From the table]

So, the rule that describes the relationship between wages and the number of hours is, wages = 8 × number of hours.


Correct answer : (3)
 50.  
The table represents the relationship between x and y.
x- 1123
y5789

Which of these equations best represents the relationship?
a.
y = x + 6
b.
y = - x - 5
c.
y = 2x + 2
d.
y = 3x + 3


Solution:

The values of y obtained when x = -1, 1, 2, 3 in y = 2x + 2 are 0, 4, 6, 8.

The values of y obtained when x = -1, 1, 2, 3 in y = 3x + 3 are 0, 6, 9, 12.

The values of y obtained when x = -1, 1, 2, 3 in y = -x - 5 are -4, -6, -7, -8

The values of y obtained when x = -1, 1, 2, 3 in y = x + 6 are 5, 7, 8, 9.

The values of y obtained for the equation y = x + 6 are same as that of the values given in the table.

So, the equation y = x + 6 best represents the given table.


Correct answer : (1)

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