Finding the Rule of a Function Table-Gr 8-Solved Examples

Solved Examples and Worksheet for Finding the Rule of a Function Table

Q1Which of the following rules describes the best input - output relationship from the table?

Input	Output
6	5
11	10
15	14
7	6

A. Output = 3 - Input
B. Output = 1 - Input
C. Output = Input - 1
D. Output = Input + 1

Solutions

Step: 1

On observing the table, it is found that the output 5 = 6 - 1, 10 = 11 - 1, 14 = 15 - 1 and 6 = 7 - 1

Step: 2

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

Correct Answer is : Output = Input - 1

Q2Mr. Nathan requires x gallons of milk for their family. The cost of x gallons of milk is given by f(x) = 1.19x. Which of the tables best suits the equation?

A. Table 1
B. Table 2
C. Table 3
D. Table 4

Solutions

Step: 1

f(x) = 1.19x

[Original equation.]

Step: 2

f(1)= 1.19(1) = 1.19

[Substitute 1 for x and simplify.]

Step: 3

f(2) = 1.19(2) = 2.38

[Substitute 2 for x and simplify.]

Step: 4

f(3) = 1.19(3) = 3.57

[Substitute 3 for x and simplify.]

Step: 5

f(4)= 1.19(4) = 4.76

[Substitute 4 for x and simplify.]

Step: 6

Table 3 matches with the equation.

Correct Answer is : Table 3

Q3Write a rule for the linear function in the table.

A. f(x) = 4x - 1
B. f(x) = 3x + 1
C. f(x) = 2x + 3
D. None of the above

Solutions

Step: 1

The formula to write a function rule from a table is f(x) = mx + b.

Step: 2

Step: 3

The value of x increases by 3 and the f(x) value increases by 12.

Step: 4

m = 123 = 4

[m = difference between f(x) values / difference between x values.]

Step: 5

When x = 0, f(x) = -1

Step: 6

b = -1

[Since b is the value of f(x) when x = 0.]

Step: 7

The rule for the linear function is f(x) = 4x - 1.

Correct Answer is : f(x) = 4x - 1

Q4Which of the following rules describes the input - output relationship from the table?

Input	Output
5	5
6	6
7	7
8	8
9	9

A. Output = Input2
B. Output = Input + 1
C. Output = Input - 1
D. Output = Input

Solutions

Step: 1

On observing the table it is found that the output 5 = 5, 6 = 6, 7 = 7, 8 = 8 and 9 = 9.

Step: 2

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

Correct Answer is : Output = Input

Q5Which equation satisfies the input-output table?

Input(x)	0	1	2	3	4	5
Output(y)	50	48	46	44	42	40

A. y = 50 - 3x
B. y = 50 - 2x
C. y = 50 - 4x
D. y = 50 - 5x

Solutions

Step: 1

y = 50 - 3x

[Consider choice A.]

Step: 2

y = 50 - 3(0) = 50

[Replace x with 0.]

Step: 3

y = 50 - 3(1) = 47

[Replace x with 1.]

Step: 4

In the table for x = 1, y = 48. So first equation is ruled out.

Step: 5

y = 50 - 2x

[Consider choice B.]

Step: 6

y = 50 - 2(0) = 50

[Replace x with 0.]

Step: 7

y = 50 - 2(1) = 48

[Replace x with 1.]

Step: 8

y = 50 - 2(2) = 46

[Replace x with 2.]

Step: 9

y = 50 - 2(3) = 44

[Replace x with 3.]

Step: 10

y = 50 - 2(4) = 42

[Replace x with 4.]

Step: 11

y = 50 - 2(5) = 40

[Replace x with 5.]

Step: 12

The equation y = 50 - 2x satisfies the table.

Correct Answer is : y = 50 - 2x

Q6Choose a rule for the linear function in the table shown.

A. f(x) = - 2x - 1
B. f(x) = 2x + 3
C. f(x) = 12x - 1
D. f(x) = 2x + 1

Solutions

Step: 1

The formula to write a function rule from a table is f(x) = mx + b.

Step: 2

Step: 3

The value of x increases by 1 and the f(x) value increases by 2.

Step: 4

m = 21 = 2

[m = difference between f(x) valuesdifference between x values.]

Step: 5

When x = 0, f(x) = 1

Step: 6

b = 1

[Since b is the value of f(x) when x = 0.]

Step: 7

The rule for the linear function is f(x) = 2x + 1.

Correct Answer is : f(x) = 2x + 1

Q7Identify the equation that satisfies the input-output table given below.

Input(x)	0	1	2	3	4	5
Output(y)	50	46	42	38	34	30

A. y = 50 - 5x
B. y = 50 - 4x
C. y = 50 - 6x
D. y = 50 - 7x
E. y = 50 - 8x

Solutions

Step: 1

Consider choice A,
y = 50 - 5x.

Step: 2

Substitute 0 for x,
50 - 5(0) = 50.

Step: 3

Substitute 1 for x,
y = 50 - 5(1) = 45.

Step: 4

In the given table for x = 1, y = 46. So first equation is ruled out.

Step: 5

Consider choice B,
y = 50 - 4x.

Step: 6

Substitute 0 for x,
y = 50 - 4(0) = 50.

Step: 7

Substitute1 for x,
y = 50 - 4(1) = 46.

Step: 8

Substitute 2 for x,
y = 50 - 4(2) = 42.

Step: 9

Substitute 3 for x,
y = 50 - 4(3) = 38.

Step: 10

Substitute 4 for x,
y = 50 - 4(4) = 34.

Step: 11

Substitute 5 for x,
y = 50 - 4(5) = 30.

Step: 12

The equation y = 50 - 4x satisfies the given table.

Correct Answer is : y = 50 - 4x

Q8What is the rule for the following table?

A	B
542	530
426	--
368	356
225	213

A. subtract 13 from the number in column A
B. subtract 11 from the number in column A
C. subtract 12 from the number in column A
D. subtract 10 from the number in column A

Solutions

Step: 1

The rule for the pattern is subtract 12 from the number in column A to get the number in column B.
542 - 12 = 530, 368 - 12 = 356, 225 - 12 = 213.

Step: 2

The missing number is 414.

Step: 3

So, the rule for the pattern is subtract 12 from the number in column A to get the number in column B

Correct Answer is : subtract 12 from the number in column A

Q9Find a rule for the table.

A. multiply by 8
B. divide by 4
C. subtract 5
D. add 10

Solutions

Step: 1

By dividing the values in column X by 4, we get the corresponding values in Column Y.

Correct Answer is : divide by 4

Q10Identify the equation that represents the values in the function table shown.

x	10	25	35	45
y	2	5	7	9

A. y = 5x
B. y = 5x
C. y = x5
D. y = x - 5

Solutions

Step: 1

On observing the table it is found that 2 = 105, 5 = 255, 7 = 355, 9 = 455.

Step: 2

So, the equation that represents the table is y = x5.

Correct Answer is : y = x5

Q11Identify the equation that represents the table.

x	6	9	12	15
y	4	5	6	7

A. y = x + 2
B. y = 3x - 1
C. y = x3 + 2
D. y = 3(x + 1)

Solutions

Step: 1

On observing the table it is found that 4 = 63 + 2, 5 = 93 + 2, 6 = 123 + 2, 7 = 153 + 2.

Step: 2

So, the equation that represents the table is y = x3 + 2.

Correct Answer is : y = x3 + 2

Q12What is the rule for the table?

Input	3	5	6	8
Output	9	13	15	19

A. Add 3 and subtract 3.
B. Divide by 3 and add 2.
C. Multiply by 1 and add 2.
D. Multiply by 2 and add 3.

Solutions

Step: 1

Consider the first input value given in the table and try each rule on the value to check if we get the corresponding output value.

Step: 2

Consider 3.
(3 + 3) - 3 = 3, not 9. So, choice 1 does not work.

Step: 3

(3 ÷ 3) + 2 = 3, not 9. So, choice 2 does not work.

Step: 4

(3 × 1) + 2 = 5, not 9. So, choice 3 does not work.

Step: 5

(3 × 2) + 3 = 9, choice 4 works.

Step: 6

So, 'multiply by 2 and add 3' is the rule for the table.

Correct Answer is : Multiply by 2 and add 3.

Q13Andrew deposited $20 initially in his bank account. Then he deposited $15 every week. The total savings, 'c' is represented by the equation, c = 20 + 15n, where 'n' denotes the number of weeks. Which table of values satisfies the equation?

A. Table 1
B. Table 3
C. Table 4
D. Table 2

Solutions

Step: 1

Substitute from 0 to 5 for 'n' in the equation.

Step: 2

You get the following table of values.

Step: 3

Compare the labels and values in this table with the tables given in the question.

Step: 4

Notice that only table 1 matches our table.

[Table 4 has n = 6 instead of 5. For n = 6, c = 110.]

Correct Answer is : Table 1

Q14The table represents the relationship between x and y.

x	- 1	1	2	3
y	5	7	8	9

Which of these equations best represents the relationship?

A. y = 3x + 3
B. y = x + 6
C. y = 2x + 2
D. y = - x - 5

Solutions

Step: 1

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

Step: 2

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

Step: 3

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

Step: 4

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

Step: 5

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

Step: 6

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

Correct Answer is : y = x + 6

Q15Which of the equations best represents the rule for the table?

x	1	2	3	4
y	8	16	24	32

A. y = 8x
B. y = 8x + 5
C. y = 3x + 7
D. y = x + 7

Solutions

Step: 1

The values of y obtained when x = 1, 2, 3, 4 in y = 3x + 7 are 10, 13, 16, 19.

Step: 2

The values of y obtained when x = 1, 2, 3, 4 in y = x + 7 are 8, 9, 10, 11.

Step: 3

The values of y obtained when x = 1, 2, 3, 4 in y = 8x + 5 are 13, 21, 29, 37.

Step: 4

The values of y obtained when x = 1, 2, 3, 4 in y = 8x are 8, 16, 24, 32.

Step: 5

The values of y obtained for the equation y = 8x are same as that of the values given in the table.

Step: 6

So, the equation y = 8x best represents the given table.

Correct Answer is : y = 8x

Solved Examples and Worksheet for Finding the Rule of a Function Table

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