Review all 3 exams and all 3 review sheets a Is y a function

Review all 3 exams and all 3 review sheets. a. Is y a function of x? (vertical line test, y^2 = x, tables of data) b. Story problems involving more than one function type (exam 1) A group on campus will make and sell bracelets to benefit a charity. The profit from selling the bracelets will go to the charity. The group members are trying to decide how much to charge (x) for each bracelet, so they took a survey to find out how many bracelets (f(x)) they would sell when the price per bracelet was x dollars. Here is what their data shows: a. What type of graph is this? b. Find a formula for f(x). c. Explain the meaning of the slope in the context of the bracelet sales. [make sure you explain the number value of the slope]. d. Explain the meaning of the y-intercept in the context of the bracelet sales. [make sure you explain the number value of the y-intercept] e. Find the x-intercept. Explain the meaning of the x-intercept in the context of the bracelet sales. f. What would be an equation for the total income of selling bracelets priced at x dollars? g. If each bracelet costs the group $1 in materials to produce, what would be an equation for the total profit as a function of the price x?

Solution

a) slope between two sets of ( x, f(x) )

slope = (195 - 240)/(3.5 - 2) = -30

Its a linear function

b) formula f(x) = mx + c

f(x) = -30x + c. Find c:

240 = -60 + c ; c= 300

f(x) = -30x +300

c) slope interpretation : It means for each dollar increase in price per bracelet , the no. of bracelets

sold decreased by 30

d) y intercept : f(0) = 300.It means intiall they had 300 bracelets

e) x intercept means when: f(x)=0

x= 10 .When the price was $10 , no bracelets were sold

f) Total income = x*f(x) = x(-30x + 300) = -30x^2 + 300x

g) Total profit = income - cost = (-30x^2 + 300x) - x*1