# Function Worksheet - Page 9

Function Worksheet
• Page 9
81.
Which of the following function rules satisfies the graph?

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

82.
Which of the following function rules satisfies the graph?

 a. Output = $\frac{input}{2}$ b. Output = Input + 2 c. Output = Input - 2 d. Output = Input2 /2

#### 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 square of the input, we can write output = input2 /2.

So, the function rule that satisfies the graph is output = input2 /2.

83.
The graph shows the relationship between distance and time for a truck driven at a constant speed. Make a table for the function and write a rule to represent the function.

 a. Distance = 15 + time b. Distance = 15 × Time c. Distance = 5 × Time d. Distance = Time - 5

#### Solution:

A function is an entity, which gives the relationship between output(Distance) and input(Time).

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

As the Distance traveled is 15 times the time taken, we can write Distance = 15 × time.

So, the function rule that represents the graph is distance = 15 × time.

84.
Which of the following rules describes the input - output relationship from the table?
 Input Output 2 8 3 12 4 16 5 20 6 24
 a. Output = Input b. Output = Input × 4 c. Output = Input + 4 d. Output = $\frac{Input}{4}$

#### Solution:

On observing the table, it is found that the output 8 = 4 × 2, 12 = 4 × 3, 16 = 4 × 4, 20 = 4 × 5 and 24 = 4 × 6.

So, we can write the relationship between input and output as a rule, Output = 4 × input.

85.
Which of the following rules describes the input - output relationship from the table?
 Input Output 20 5 24 6 28 7 32 8 36 9
 a. Output = Input × 4 b. Output = Input + 4 c. Output = $\frac{Input}{4}$ d. None of the above

#### Solution:

On observing the table it is found that the output 5 = 20 / 4, 6 = 24 / 4, 7 = 28 / 4, 8 = 32 / 4 and 9 = 36 / 4.

So, we can write the relationship between input and output as a rule, Output = Input / 4.

86.
Which of the following rules describes the input - output relationship from the table?
 Input Output 4 4 5 5 6 6 7 7 8 8
 a. Output = Input - 1 b. Output = Input c. Output = $\frac{Input}{2}$ d. Output = Input + 1

#### Solution:

On observing the table it is found that the output 4 = 4, 5 = 5, 6 = 6, 7 = 7 and 8 = 8.

So, we can write the relationship between input and output as a rule, Output = input.