Input | Output |

6 | 5 |

11 | 10 |

15 | 14 |

7 | 6 |

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

Step: 1

[Original equation.]

Step: 2

[Substitute 1 for x and simplify.]

Step: 3

[Substitute 2 for x and simplify.]

Step: 4

[Substitute 3 for x and simplify.]

Step: 5

[Substitute 4 for x and simplify.]

Step: 6

Table 3 matches with the equation.

Correct Answer is : Table 3

Step: 1

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

Step: 2

Step: 3

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

Step: 4

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

Step: 5

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

Step: 6

[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

Input | Output |

5 | 5 |

6 | 6 |

7 | 7 |

8 | 8 |

9 | 9 |

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

Input( | 0 | 1 | 2 | 3 | 4 | 5 |

Output( | 50 | 48 | 46 | 44 | 42 | 40 |

Step: 1

[Consider choice A.]

Step: 2

[Replace x with 0.]

Step: 3

[Replace x with 1.]

Step: 4

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

Step: 5

[Consider choice B.]

Step: 6

[Replace x with 0.]

Step: 7

[Replace x with 1.]

Step: 8

[Replace x with 2.]

Step: 9

[Replace x with 3.]

Step: 10

[Replace x with 4.]

Step: 11

[Replace x with 5.]

Step: 12

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

Correct Answer is : y = 50 - 2x

Step: 1

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

Step: 2

Step: 3

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

Step: 4

[m = d i f f e r e n c e b e t w e e n f ( x ) v a l u e s d i f f e r e n c e b e t w e e n x v a l u e s .]

Step: 5

When x = 0, f (x ) = 1

Step: 6

[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

Input( | 0 | 1 | 2 | 3 | 4 | 5 |

Output( | 50 | 46 | 42 | 38 | 34 | 30 |

Step: 1

Consider choice A,

y = 50 - 5x .

Step: 2

Substitute 0 for x ,

50 - 5(0) = 50.

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

A | B |

542 | 530 |

426 | -- |

368 | 356 |

225 | 213 |

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.

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

10 | 25 | 35 | 45 | |

2 | 5 | 7 | 9 |

Step: 1

On observing the table it is found that 2 = 10 5 , 5 = 25 5 , 7 = 35 5 , 9 = 45 5 .

Step: 2

So, the equation that represents the table is y = x 5.

Correct Answer is : y = x 5

6 | 9 | 12 | 15 | |

4 | 5 | 6 | 7 |

Step: 1

On observing the table it is found that 4 = 6 3 + 2, 5 = 9 3 + 2, 6 = 12 3 + 2, 7 = 15 3 + 2.

Step: 2

So, the equation that represents the table is y = x 3 + 2.

Correct Answer is : y = x 3 + 2

Input | 3 | 5 | 6 | 8 |

Output | 9 | 13 | 15 | 19 |

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.

(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.

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

- 1 | 1 | 2 | 3 | |

5 | 7 | 8 | 9 |

Which of these equations best represents the relationship?

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

1 | 2 | 3 | 4 | |

8 | 16 | 24 | 32 |

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

- Determining Whether a given Relation is a Function-Gr 8-Solved Examples
- Classifying Relations as Linear or Nonlinear-Gr 8-Solved Examples
- Identifying Functions-Gr 8-Solved Examples
- Graphing Linear Functions for a Given Domain-Gr 8-Solved Examples
- Graphing Linear Functions based on an x/y Table-Gr 8-Solved Examples
- Graphing Linear Equations-Gr 8-Solved Examples
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- Representing Exponential Functions Using Tables or Graphs-Gr 8-Solved Examples

- Operation
- Order Of Operations
- Rule