X | Y |

0 | 30 |

1 | 27 |

2 | 24 |

3 | 21 |

4 | 18 |

ii.) The function whose input and output are related by

Step: 1

From function1, Mary has $30 and spends money each week. The amount of money left from her and $3 decreases each week.

Step: 2

So, the graph has a negative slope of -3.

Step: 3

From function 2, y = 2x +4 which is in the form of y = mx + c . This function has a positive slope of 2.

Step: 4

Function 1 has a negative slope.

Correct Answer is : (i)

(i) The school book store rents graphing calculators for $4 per month. It also collects a non- refundable fee of $5 for the school year. The total cost y of renting a calculator is modeled by function 1 where x denotes the number of months.

(ii) The graph of function 2 is as shown.

Step: 1

The graph of function 2 contains (0, 1) and (1, 3).

[From graph]

Step: 2

So, slope of the graph that represents function 2 = 3 - 1 1 - 0 = 2 1 = 2

[m = y 2 - y 1 x 2 - x 1 ]

Step: 3

So, the rate of change of function 2 is 2.

Step: 4

From the description of function 1, it can be represented as y = 4x + 5, where y denotes total cost of renting and x denotes number of months.

Step: 5

So, the rate of change of function 1 is 4.

Step: 6

Therefore, function 1 has greater rate of change.

[4 > 2]

Correct Answer is : Function 1

(i) Function 1 is represented by the table shown.

1 | 2 | 3 | 4 | 5 | |

3 | 4 | 5 | 6 | 7 |

(ii)The graph of function 2 is a shown.

Step: 1

Linear equation in intercept form is y = a + bx , where b is the rate of change and a is the y - intercept.

Step: 2

From the table, change in output values = 1

Step: 3

Change in input values = 1

Step: 4

Rate of change = C h a n g e i n o u t p u t v a l u e s C h a n g e i n i n p u t v a l u e s = 1 1 = 1

Step: 5

Working backwards with the values in the table, we get (0, 2). So, the y -intercept is 2.

Step: 6

So, the function 1 that satisfies the table is y = x + 2, which is a linear equation. So, function 1 is linear.

Step: 7

Correct Answer is : Function 1

(i) Josh counted that the number of students who participated in different sports are 2, 4, 6, 8, and 10 respectively. The situation is modeled by function 1 as

(ii)The graph of function 2 is as shown.

Step: 1

A function such that f (x ) = f (- x ) where the value remains unchanged if the sign of the independent variable is reversed.

Step: 2

If we observe the given functions 1 and 2, we will notice that Function 2 is an even function.

Correct Answer is : Function 2

(i) Wilma had $8 with her. She sold x cards at $4 each and earned some money. The money she had with her finally is modeled by function 1 is

(ii) Function 2 is given by

Step: 1

Linear equation in intercept form is y = a + bx , where b is the rate of change and a is the y - intercept.

Step: 2

Function 1 is given by y = 4x + 8. So, rate of change of function 1 is 4, which is a constant.

Step: 3

The function 2, y = x ^{2} is a quadratic function. So, it has no constant rate of change.

[Nonlinear functions are functions that do not have constant rate of change.]

Step: 4

So, function 1 has a constant rate of change.

Correct Answer is : Function 1

(i) Function 1 is represented by the table that shows the relationship between time and volume for a tank that is filling with water.

Time | 1 | 2 | 3 | 4 | 5 |

Volume | 4 | 8 | 12 | 16 | 20 |

(ii) Function 2 is given by

Step: 1

Linear equation in intercept form is y = a + bx , where b is the rate of change and a is the y - intercept.

Step: 2

From the table, change in output values = 4

Step: 3

Change in input values = 1

Step: 4

Rate of change = C h a n g e i n o u t p u t v a l u e s c h a n g e i n i n p u t v a l u e s = 4 1 = 4

Step: 5

Working backwards with the values in the table, we get (0, 0). So, the y -intercept is 0.

Step: 6

So, the function 1 that satisfies the table is y = 4x , which is a linear equation.

Step: 7

Function 2 is given by y = -2x + 5, which is in the form y = a + bx . So, it is also a linear function.

Step: 8

If the graph of a function has positive slope, then that function is said to be an increasing function.

Step: 9

Slope of function 1 is 4(>0). So it is an increasing function.

Step: 10

Slope of function 2 is -2(<0). So it is not an increasing function.

Correct Answer is : Function 1

(i) Function 1 is represented by the table that shows the relationship between the age of a mother and her child on her child's birthday.

Child's age | 1 | 2 | 3 | 4 | 5 |

Mothers age | 23 | 24 | 25 | 26 | 27 |

(ii) The graph of function 2 is as shown.

Step: 1

Step: 2

From the table, change in output values = 1

Step: 3

Change in input values = 1

Step: 4

Rate of change = C h a n g e i n o u t p u t v a l u e s C h a n g e i n i n p u t v a l u e s = 1 1 = 1

Step: 5

Working backwards with the values in the table, we get (0, 22). So, the y -intercept is 22.

Step: 6

So, the function 1 that satisfies the table is y = x + 22, which is a linear equation.

Step: 7

The graph of function 2 contains (0, -1) and (-1, 1).

[From graph]

Step: 8

So, slope of the graph that represents function 2 = 1 - ( - 1 ) - 1 - 0 = 2 - 1 = - 2.

[m = y 2 - y 1 x 2 - x 1 ]

Step: 9

The graph of function 2 contains (0, -1). So, the y - intercept is -1.

[y -intercept is the y - value when x = 0]

Step: 10

So, the function 2 that satisfies the graph is y = -2x - 1, which is a linear equation. So, function 2 is linear.

Step: 11

If the graph of a function has positive slope, then that function is said to be an increasing function.

Step: 12

Slope of function 1 is 1(>0). So it is an increasing function.

Step: 13

Slope of function 2 is -2(<0). So it is a decreasing function.

Correct Answer is : Function 2

(i) Function 1 is given by

(ii) The graph of function 2 is as shown.

Step: 1

The graph of function 2 contains (-2, 4), (-1, 1), (0, 0), (1, 1) and (2, 4).

[From graph]

Step: 2

From these points, it can be observed that y -coordinate of each point is equivalent the square of corresponding x - coordinate.

[4 = (-2)^{2} = (2)^{2}; 1 = (-1)^{2} = (1)^{2}]

Step: 3

So, the function 2 that satisfies the graph is y = x ^{2}.

Step: 4

A function y = f (x ) is said be an odd function, if f (-x ) = -f(x ), for all x in the domain of f .

Step: 5

Function 1 is given by y = f (x ) = sin x

Step: 6

For function 1, f (-x ) = sin(-x ) = - sin x = - f (x )

Step: 7

So, function 1 is an odd function.

[f (-x ) = -f (x )]

Step: 8

For function 2, f (-x ) = (-x )^{2} = x ^{2} = f (x )

Step: 9

So, function 2 is an even function.

[f (-x ) = f (x )]

Correct Answer is : Function 1

(i). The table shows the values of a function

X | Y |

-1 | 1 |

0 | 0 |

1 | -1 |

2 | -2 |

3 | -3 |

Where

Step: 1

From the function y = - [x] has greatest integer symbol. So this is a greatest integer function.

Correct Answer is : i

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