Learn about Function with Constants Functions with Constants. So in this problem it states that a fifth grade student helps reduce thrash by recycling. Each week she collects 10 pounds of newspapers from her family. Each neighbor gives her an additional 3 pounds of newspaper each week. How many pounds of paper does she collect in all, if she collects from 5 neighbors? In this problem, we need to find out the number of pounds of newspaper the fifth grade student collects in a week. The amount of newspaper is equal to 10+3 times the number of neighbors. So the amount of newspaper is equal to 10+3 times the amount of neighbors. This is an example of a function. So the number of pounds of paper collected when the number of neighbors is zero is 10 because we know that each week she collects 10 pounds of papers from her family. So she collects the 10 pounds of papers without the neighbors, so the amount of paper collected when the numbers are zero is 10. So that means the number of pounds of paper collected when the number of neighbors is 1 will be 10+1×3. So its 10+3 times the number of neighbors. So its 10+1 neighbor times 3 which is 13. So the same trend follows for the higher number of neighbors. We can completely solve the equation using a function table. So here is our function table. So each number in the number of neighbor’s row is multiplied by 3 and added to 10 to find the number in the pounds row. Each number is multiplied by 3, so you multiply it by 3, so 0×3 is 0 and you add 10 is 10. 1×3 is 3+10 is 13, and so forth. If we continue this pattern, then the number of pounds collected with 5 neighbors is 25 pounds. Now, we can also use an equation to solve this problem, so let’s go ahead and solve this using an equation. To solve an equation, the first step we need to do is to define a variable or define our variables. So we’re going to let the number of pounds of newspapers collected is going to be N, alright and the number of neighbors she collects newspapers from, - we’re going to let that be represented by C. Now we’ve defined our variables, so our next step is we need to write an equation. So we know that from before, we know that the amount of newspapers is equal to 10+3 times the number of neighbors. So this is our function, we know that the amount of newspaper is equal to 10+3 times the number of neighbors. So, we know that the number of the amount of newspaper, so the pounds collected, the numbers of newspaper N is equal to and we said 10+3 times the number of neighbors collected from. So then it would be 3 times the number of neighbors collected from, so be 3×c. So here we have our equation, the equation shows that for unique value of c, there’s exactly one value of N. So here we have our equation. So our next step, step 3, is we are going to substitute our variables. We need to find the pounds of newspapers that are collected if she collects 5 neighbors. So we’re looking for 5 neighbors. So we’re going to let c=5, the number of neighbors collected because we want to know from our problem how many she collects in 5 neighbors. So we’re going to go ahead and plug in from our problem. So n=10+3×c and we know that c=5. So it’s going to be n=10+, right and when 3 is written next to or when a variable is written next to a number, it’s times. So be n=10+3×5. So we do our multiplication first, so be n=10+15 and then n=25. So the number of pounds of newspapers collected if she collects from 5 neighbors is 25. So our answer would be 25 pounds, the number of pounds would be25. Things to remember is that to find the relationship between two functions, we use a table. A function is an equation that gives the relationship between variables and represents a situation. So remember a function is an equation between two variables that represents a situation. The value of a function can be calculated by substituting the value of the unknown variables. Now for unique value of a variable, there is only one value for the function.