1) Create and justify a relation that represents a function with the given range. Write your answers as ordered pairs.

a)
{ (0 , 11) , (1 , 20) , (2 , 34) , (3 , 41) } this is because no value is same for the order pairs in x values

b)Create and justify a relation that does not represent a function with the given range. Write your answers as ordered pairs.
{ (0 , 11) , (0 , 20) , (2 , 34) , (3 , 41) } this is the case since the values of X in the first two cases are similar hence making it not be a function

2) Find the equation of the line in the graph, and mathematically model the scenario using function notation where cost is a function of number of minutes.
We start by calculating the slope m = (40 - 20)/(400 - 0) m = 20/400 m = 2/40 m = 1/20 the form of the equation is given as; y = mx + b where m is the slope hence m = 1/20 , (0 , 20) y = (1/20)x + 20

3) A textbook company keeps track of its daily cost for printing whole textbooks to different schools, but can only print up to 500 books a day. The daily cost (C) to print x number of textbooks is given by C(x) = 3.50x + 1200.

A.
a) Using the function, determine one possible daily cost by evaluating the function for any input of your choice with four text books as x = 4, the cost is :
C(4) = 3.50 * 4 + 1200
C(4) = 14 + 1200
C(4) = $ 1214

b) For what value of x does C(x) = 1900
C(x) = 3.50x + 1200 when C(x) = 1900
1900 = 3.50x + 1200
1900 - 1200 = 3.50x
700 = 3.50x
700/3.5 = x
200 books = x

c) Interpret the statement C(20) = 1270.

when x = 20 books, the cost is $1270

d) Interpret the statement C(w) = p when x = w books, the cost is $ p

e) Explain whether C(40.5) = 1341.75 is correct and possible given the context of this problem.

we can't have 40.5 books since we will need to either have a whole book but not a fraction. Hence the statement is wrong.

4) Bill is able to save $35/week after working part-time and paying his expenses. These two formulas show his weekly savings:
1) Which one of these formulas show the sequence written recursively, and which shows it written explicitly? Justify your explanations
Recursive: A. f(1) = 35, f(n) = f(1) + f(n-1) for n > 1 the values are dependent on previously done calculations.

Explicit: f(n) = 35n since it depends on its own.

2) Use the recursive formula to make a table of values for 1 ≤ n ≤ 5. Show your calculations. Explain what your table means n is the number of weeks f(1) = 35 the first week, he save $35

f(2) = f(1) + f(2-1) for n = 2 f(2) = f(1) + f(1) f(2) = 35 + 35 f(2) = $ 70 the second week, he saves $70

f(3) = f(1) + f(3-1) for n = 3 f(3) = f(1) + f(2) f(3) = 35 + 70 f(3) = $ 105 the third week, he saves $ 105

f(4) = f(1) + f(4-1) for n = 4 f(4) = f(1) + f(3) f(4) = 35 + 105 f(4) = $ 140 the fourth week, he saves $ 140

f(5) = f(1) + f(5-1) for n = 5 f(5) = f(1) + f(4) f(5) = 35 + 140 f(5) = $ 175 the fifth week, he saves $ 175

So the amounts from the above calculations for week 1 to week 5 are given as; I. 35,70,105,140 and 175 respectively.

3) Use any formula of your choice to find f(40). Explain why you chose that method and what your answer means. Show your calculations. I. f(40) = 35 * 40 f(40) = $ 1400 in 40 weeks, he will save $ 1400 this is because the formula f(n)= 35n has been simplified for larger numbers and will give the same values as recursive calculations.

4) Given the sequence of numbers: 5, 6, 8, 11, 15, 20, 26, 33, 41,… Explain whether or not this sequence can be considered a function. (1 , 5) , (2 , 6) , (3, 8), .... yes since my domain or x-axis are not paired with y-values. it is function

5) Create your own equation written in standard form
4x + 10y = 20 this is the Standard Form

x-intercept means y = 0
4x + 0 = 20 this would imply that x = 5 as (5 , 0)

y-intercept means x = 0
0 + 10y = 20 this will subsequently imply that y = 2 as (0 , 2)

function Notation:
4x + 10y = 20
10y = 20 - 4x y = (20 - 4x)/10 y = 20/10 - 4x/10 y = 2 - (2/5)x y(x) = 2 - (2/5)x this is the function notation

Graph:

6.) Compare the graph from question 2 and the equation from question 5. How are the graphs similar and different? Determine which has the greater y-value when x is 160, and explain how you determined it.

y(x) = (1/20)x + 20 when x = 160 y(160) = (1/20) * 160 + 20 y(160) = 8 + 20 y(160) = 28 as the y value when x=160 and y = 2 - (2/5)x ----> x = 160 y = 2 - 64 y = - 62 as the y value when x=160 hence the value from equation 2 is greater than that of equation 5. Hence we can say that equation number 2 is increasing, while equation in 5 is decreasing.