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 linear function.
Step-by-step solution:-
From the given table, we observe the following readings-
x1 = -2, y1 = -20;
x2 = 0, y2 = -6;
x3 = 2, y3 = 8;
x4 = 4, y4 = 22;
x5 = 6, y5 = 36
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 0 - (-2) = 0 + 2 = 2
dx2 = x3 - x2 = 2 - 0 = 2
dx3 = x4 - x3 = 4 - 2 = 2
dx4 = x5 - x4 = 6 - 4 = 2
Difference between 2 consecutive y values-
dy1 = y2 - y1 = -6 - (-20) = -6 + 20 = 14
dy2 = y3 - y2 = 8 - (-6) = 8 + 6 = 14
dy3 = y4 - y3 = 22 - 8 = 14
dy4 = y5 - y4 = 36 - 22 = 14
We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is constant i.e. 14.
Hence, the given function is a linear function.
Final Answer:-
∴ The given function is a linear function.
x2 = 0, y2 = -6;
x3 = 2, y3 = 8;
x4 = 4, y4 = 22;
x5 = 6, y5 = 36
a). Difference between 2 consecutive x values-
dx1 = x2 - x1 = 0 - (-2) = 0 + 2 = 2
dx2 = x3 - x2 = 2 - 0 = 2
dx3 = x4 - x3 = 4 - 2 = 2
dx4 = x5 - x4 = 6 - 4 = 2
Difference between 2 consecutive y values-
dy1 = y2 - y1 = -6 - (-20) = -6 + 20 = 14
dy2 = y3 - y2 = 8 - (-6) = 8 + 6 = 14
dy3 = y4 - y3 = 22 - 8 = 14
dy4 = y5 - y4 = 36 - 22 = 14
We observe that the difference for every consecutive x values is constant i.e. 1 and for y values the difference is constant i.e. 14.
Hence, the given function is a linear function.
Final Answer:-
∴ The given function is a linear function.
Related Questions to study
Jamie will choose between two catering companies for an upcoming party. Company A charges a set up fee of $ 500 plus $25 for each guest. Company B charges a set up fee of $200 plus $ 30 per guest
a) Write expression that you can use to determine the amount each company charges for g guests .
b) Jamie learns that the $ 500 set up fee for company A includes payment for 20 guests. The $25 per guests charge is for every guest over the first 20.If there will be 50 guests , which company will cost the least ? Explain.
In this question, the answer is to find out with the help of the fixed cost and variable cost formulas. So let's first understand what variable and fixed costs mean and the formula to calculate costs.
Variable costs are expenses that varies in proportion to the number of goods or services produced by a company. In other words, they are costs that vary with the amount of activity. As a result, the costs rise as the volume of activities rises and fall as the volume of activities falls.
Total Variable Cost = Total Output Quantity x Variable Cost Per Unit Output.
A fixed cost is any business expense that does not change in response to production or sales. Fixed costs are also known as indirect costs or overhead. Fixed costs cannot be changed to reduce expenses. Instead, they typically rely on an outside entity, such as a landlord or bank. Fixed costs include rent, insurance, and labor costs.
Fixed cost = Total cost of production - (No. of units produced x Variable cost per unit)
To find the total cost,
Total cost= Fixed cost + Variable cost
Jamie will choose between two catering companies for an upcoming party. Company A charges a set up fee of $ 500 plus $25 for each guest. Company B charges a set up fee of $200 plus $ 30 per guest
a) Write expression that you can use to determine the amount each company charges for g guests .
b) Jamie learns that the $ 500 set up fee for company A includes payment for 20 guests. The $25 per guests charge is for every guest over the first 20.If there will be 50 guests , which company will cost the least ? Explain.
In this question, the answer is to find out with the help of the fixed cost and variable cost formulas. So let's first understand what variable and fixed costs mean and the formula to calculate costs.
Variable costs are expenses that varies in proportion to the number of goods or services produced by a company. In other words, they are costs that vary with the amount of activity. As a result, the costs rise as the volume of activities rises and fall as the volume of activities falls.
Total Variable Cost = Total Output Quantity x Variable Cost Per Unit Output.
A fixed cost is any business expense that does not change in response to production or sales. Fixed costs are also known as indirect costs or overhead. Fixed costs cannot be changed to reduce expenses. Instead, they typically rely on an outside entity, such as a landlord or bank. Fixed costs include rent, insurance, and labor costs.
Fixed cost = Total cost of production - (No. of units produced x Variable cost per unit)
To find the total cost,
Total cost= Fixed cost + Variable cost
For how many games is the total cost of bowling equal for the two bowling establishments ?
For how many games is the total cost of bowling equal for the two bowling establishments ?
Solve the radical equation 
Check for extraneous solutions
Solve the radical equation Check for extraneous solutions
Solve 8X-4= 2(4X-4)
Solve 8X-4= 2(4X-4)
Determine whether a table shows a linear , quadratic or exponential function ?
Determine whether a table shows a linear , quadratic or exponential function ?
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.
Check for extraneous solutions
