Question

T-SHIRTS

A school organization has found four different places from which they may place order of t-shirts. Each function below could represent the cost of placing a t-shirt order as a function of the number of t-shirts purchased. c represents cost in dollars, t represents # of t-shirts.

A) c = 5t
B) c =3.25t + 55
C) c =3t + 100
D) c =6t - 55

DIRECTIONS FOR THE T-SHIRTS PROBLEM

Graph each function (equation)

• Graph all four functions on the same graph (color code) - by hand

• Graph data for up to 90 t-shirts at least. (use Desmos to get an overall picture of what graphs look like)

• Write a reflection for the graph

~Explanation as what the graph shows. Make sure to include:

• Comparison of costs - when is it cheapest, most expensive, etc.

-:- Give at least 6 pieces of comparison information from the graph

• What the slope represents in each function

• What the y-intercept represents in each function

Answer 1

Given functions are :

c = 5t (Violet colured line)

c =3.25t + 55 (Black coloured line)

c =3t + 100 (Red coloured line)

c =6t - 55 (Blue coloured line)

Graph of all four functions is :

Here, graph of the functions represent that total cost of t T-shirts for four different places.

number of T-shirts	Violet coloured line	Black coloured line	Red coloured line	Blue coloured line
15	75	103.75	145	35
30	150	152.5	190	125
45	225	201.25	235	215
60	300	250	280	305
75	375	298.75	325	395
90	450	347.5	370	485

Slope of each function represents the cost of every T-shirt in four different places.

The y-intercept represents either discounted charge or extra charge or no other charge.

If y-intercept is of the form y = -a, then there will be a discounted charge in total cost.

If y-intercept is of the form y = a, then there will be an extra charge.

If y-intercept is of the form y = 0, then there will be no other charge.