Question
Determine whether a table shows a linear , quadratic or exponential function ?
Hint:
1. When the difference between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant. i.e. y(n)- y(n-1) is constant for any value of n, the function is known as a linear function.
2. When the difference between 2 consecutive differences for output values (y values) for a given constant change in the input values (x values) is constant. i.e. dy(n)- dy(n-1) is constant for any value of n, the function is known as a quadratic function.
3. When the ratio between 2 consecutive output values (y values) for a given constant change in the input values (x values) is constant i.e. 
is constant for any value of n, the function is known as an exponential function.
The correct answer is: The given function is a quadratic function.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = 0, y1 = 3;
x2 = 1, y2 = 7;
x3 = 2, y3 = 19;
x4 = 3, y4 = 39;
x5 = 4, y5 = 67
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 1 - 0 = 1
dx2 = x3 - x2 = 2 - 1 = 1
dx3 = x4 - x3 = 3 - 2 = 1
dx4 = x5 - x4 = 4 - 3 = 1
Difference between 2 consecutive y values-
dy1 = y2 - y1 = 7 - 3 = 4
dy2 = y3 - y2 = 19 - 7 = 12
dy3 = y4 - y3 = 39 - 19 = 20
dy4 = y5 - y4 = 67 - 39 = 28
We observe that the difference for every consecutive x values is constant i.e. 1 but for y values the difference are not constant.
Hence, the given function is not a linear function.
b). Now, difference between 2 consecutive differences for y values-
dy2 - dy1 = 12 - 4 = 8
dy3 - dy2 = 20 - 12 = 8
dy4 - dy3 = 28 - 20 = 8
We observe that the difference of differences of 2 consecutive y values are constant i.e. 8.
Hence, the given function is a quadratic function.
b). Now, difference between 2 consecutive differences for y values-
dy2 - dy1 = 12 - 4 = 8
dy3 - dy2 = 20 - 12 = 8
dy4 - dy3 = 28 - 20 = 8
We observe that the difference of differences of 2 consecutive y values are constant i.e. 8.
Hence, the given function is a quadratic function.
Final Answer:-
∴ The given function is a quadratic function.
x2 = 1, y2 = 7;
x3 = 2, y3 = 19;
x4 = 3, y4 = 39;
x5 = 4, y5 = 67
a). Difference between 2 consecutive x values-
dx2 = x3 - x2 = 2 - 1 = 1
dx3 = x4 - x3 = 3 - 2 = 1
dx4 = x5 - x4 = 4 - 3 = 1
Difference between 2 consecutive y values-
dy2 = y3 - y2 = 19 - 7 = 12
dy3 = y4 - y3 = 39 - 19 = 20
dy4 = y5 - y4 = 67 - 39 = 28
We observe that the difference for every consecutive x values is constant i.e. 1 but for y values the difference are not constant.
Hence, the given function is not a linear function.
b). Now, difference between 2 consecutive differences for y values-
dy2 - dy1 = 12 - 4 = 8
dy3 - dy2 = 20 - 12 = 8
dy4 - dy3 = 28 - 20 = 8
We observe that the difference of differences of 2 consecutive y values are constant i.e. 8.
Hence, the given function is a quadratic function.
b). Now, difference between 2 consecutive differences for y values-
dy2 - dy1 = 12 - 4 = 8
dy3 - dy2 = 20 - 12 = 8
dy4 - dy3 = 28 - 20 = 8
We observe that the difference of differences of 2 consecutive y values are constant i.e. 8.
Hence, the given function is a quadratic function.
Final Answer:-
∴ The given function is a quadratic function.
Related Questions to study
Two window washers start at the heights shown ,one is rising , other is descending . How long does it take for the two window washers to reach the same height ? Explain.
The rate at which an object move is refers as its speed. If an object has traveled far away from the initial place and how much time it takes? To be calculated using the average speed traveled by an object. The speed formula is speed = distance/time. To determine the units for speed, we must consider the units for distance and time.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Here speed, distance, and time are internally linked. So, to calculate the value of among one, we require another unit.
For example, to determine the time required to complete a journey, we must know the distance and speed first.
Two window washers start at the heights shown ,one is rising , other is descending . How long does it take for the two window washers to reach the same height ? Explain.
The rate at which an object move is refers as its speed. If an object has traveled far away from the initial place and how much time it takes? To be calculated using the average speed traveled by an object. The speed formula is speed = distance/time. To determine the units for speed, we must consider the units for distance and time.
There are three different ways to write the formula. They are:
• speed = distance ÷ time
• distance = speed × time
• time = distance ÷ speed
Here speed, distance, and time are internally linked. So, to calculate the value of among one, we require another unit.
For example, to determine the time required to complete a journey, we must know the distance and speed first.
Solve : 2(y-6) = 3(y-4) -y
Solve : 2(y-6) = 3(y-4) -y
Solve the radical equation 
Check for extraneous solutions
Solve the radical equation Check for extraneous solutions
Solve : -3 (8+3h) = 5h+ 4
Solve : -3 (8+3h) = 5h+ 4
Solve : 5 (2X+6) = 8X+48
Solve : 5 (2X+6) = 8X+48
Solve for y where 
Solve for y where
A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains . The equations 12 + 7.6n and 6 + 8n , where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains . How many smaller boxes equal the same amount of cereal in the larger box ?
A cereal box manufacturer changes the size of the box to increase the amount of cereal it contains . The equations 12 + 7.6n and 6 + 8n , where n is the number of smaller boxes, are both representative of the amount of cereal that the new larger box contains . How many smaller boxes equal the same amount of cereal in the larger box ?
You are solving an equation with a variable on each side. Does the side on which you choose to isolate the variable affect the solution . Why might you choose one side over the other ?
You are solving an equation with a variable on each side. Does the side on which you choose to isolate the variable affect the solution . Why might you choose one side over the other ?
Solve for y where 
Solve for y where
Isabel says that the equation x-2= -(x-2) has no solution because a number can never be equal to its opposite, Explain the error Isabel made .
Isabel says that the equation x-2= -(x-2) has no solution because a number can never be equal to its opposite, Explain the error Isabel made .
Tavon has a $50 gift card that loses $2 for each 30 day period it is not used . He has $40 card that loses $1.50 for each 30 day period it is not used .
Write and solve an equation for the number of 30 day periods until the value of the gift cards will be equal ?
The quantity of goods in general that will be exchanged for one unit of money is then the value of money. Money's value is defined as its purchasing power, or the amount of goods and services it can buy.
The time value of money (TVM) is the idea that a sum of money is worth more now than it will be at a later date because of the potential earnings in the interim. A sum of money in hand is more valuable than the same sum to be paid later. The time value of money is another name for the present discounted value.
Tavon has a $50 gift card that loses $2 for each 30 day period it is not used . He has $40 card that loses $1.50 for each 30 day period it is not used .
Write and solve an equation for the number of 30 day periods until the value of the gift cards will be equal ?
The quantity of goods in general that will be exchanged for one unit of money is then the value of money. Money's value is defined as its purchasing power, or the amount of goods and services it can buy.
The time value of money (TVM) is the idea that a sum of money is worth more now than it will be at a later date because of the potential earnings in the interim. A sum of money in hand is more valuable than the same sum to be paid later. The time value of money is another name for the present discounted value.
Solve for y where 
Solve for y where
The triangle shown is isosceles. Find the length of each side and the perimeter ?
An isosceles triangle is one with two sides of the same length. An isosceles triangle's two opposite angles are equal in size.
¶Triangles are three-sided polygons that are classified into three types based on their sides, such as:
¶Triangle of Scalene (All three sides are unequal)
Triangle of isosceles (Only two sides are equal)
(All three sides are equal) Equilateral triangle
¶Triangle's isosceles perimeter in units of P = 2a + b
¶The area of an isosceles triangle
A = 1/2 x b x h Square units.
The triangle shown is isosceles. Find the length of each side and the perimeter ?
An isosceles triangle is one with two sides of the same length. An isosceles triangle's two opposite angles are equal in size.
¶Triangles are three-sided polygons that are classified into three types based on their sides, such as:
¶Triangle of Scalene (All three sides are unequal)
Triangle of isosceles (Only two sides are equal)
(All three sides are equal) Equilateral triangle
¶Triangle's isosceles perimeter in units of P = 2a + b
¶The area of an isosceles triangle
A = 1/2 x b x h Square units.
Solve for y where 
Solve for y where
Cameron pays $0.95 per song with his current music service. A new music download service charges $0.89 per song with a $12 joining fee. Should Cameron switch to the new service ? Write an equation to represent when the cost for any number of songs ,s, is the same for both services.
A service charge is a fee for services related to the primary product or service purchased. The cost charged is applicable at the time of transaction takes place. Many industries, including restaurants, banking, travel, and tourism, charge service fees. These fees may cover consumer services and administrative or processing costs when collected. Service charges are mandatory charges that are paid directly to the company. They are different from tips delivered to the employee who provides the service. The customer is entirely responsible for tipping and the amount. These are extra fees associated with the purchase of a product or service. They typically charge during the transaction between the consumer and the company.
Cameron pays $0.95 per song with his current music service. A new music download service charges $0.89 per song with a $12 joining fee. Should Cameron switch to the new service ? Write an equation to represent when the cost for any number of songs ,s, is the same for both services.
A service charge is a fee for services related to the primary product or service purchased. The cost charged is applicable at the time of transaction takes place. Many industries, including restaurants, banking, travel, and tourism, charge service fees. These fees may cover consumer services and administrative or processing costs when collected. Service charges are mandatory charges that are paid directly to the company. They are different from tips delivered to the employee who provides the service. The customer is entirely responsible for tipping and the amount. These are extra fees associated with the purchase of a product or service. They typically charge during the transaction between the consumer and the company.
