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Function Worksheets - Page 12

Function Worksheets
  • Page 12
 111.  
Valerie bought apples at $3 each. Which function represents the relation between the number of apples (a), she bought and the total cost, f(a)?
a.
f(a) = 3
b.
f(3) = a
c.
f(a) = a3
d.
f(a) = 3a


Solution:

Total cost = the cost of each apple × the number of apples she bought.

f(a) = $3 × a
[Substitute the values.]

f(a) = 3a
[Simplify.]

The function that represents a relation between the number of apples and the total cost is f(a) = 3a.


Correct answer : (4)
 112.  
Which function is best represented by the table?
InputOutput
65
1110
1615
76

a.
Output = 1 - Input
b.
Output = 3 - Input
c.
Output = Input - 1
d.
Output = Input + 1


Solution:

On observing the table, it is found that the output 5 = 6 - 1, 10 = 11 - 1, 15 = 16 - 1 and 6 = 7 - 1

So, the relation between the input and output values is Output = Input - 1.


Correct answer : (3)
 113.  
Which of the tables gives the input-output relationship for the rule y = 5x + 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.


Correct answer : (2)
 114.  
Which function is best represented by the graph?


a.
Output = Input + 2
b.
Output = Input 2
c.
Output = 2 × Input
d.
Output = Input


Solution:

A function is an entity, which gives the relationship between output and input.


From the graph, make a table of input and output values.

As the output is half of the input, we can write output = Input / 2.

So, the function rule that satisfies the graph is output = Input / 2.


Correct answer : (2)
 115.  
Which of the function tables represents the function f(x) = 5 2x, for x = 2, 4, 6, 8, and 10 as domain?


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


Solution:

f(x) = 52x
[Original function.]

x = 2, f(2) = 52 × 2 = 5
[Substitute the domain values in the function.]

x = 4, f(4) = 52 × 4 = 5(2) = 10

x = 6, f(6) = 52 × 6 = 5(3) = 15

x = 8, f(8) = 52 × 8 = 5(4) = 20

x = 10, f(10) = 52 × 10 = 5(5) = 25

The values of x and f(x) can be tabulated as shown in Table 1.

Table 1 is the function table, which describes the function.


Correct answer : (3)

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