# 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. $f$($a$) = $\frac{a}{3}$ d. $f$($a$) = 3$a$ #### 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.

112.
Which function is best represented by the table?
 Input Output 6 5 11 10 16 15 7 6

 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.

113.
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.

114.
Which function is best represented by the graph?

 a. Output = Input + 2 b. Output = $\frac{Input}{2}$ 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.

115.
Which of the function tables represents the function $f$($x$) = $\frac{5}{2}$$x$, 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.