INTERPRETING FUNCTION NOTATION WORD PROBLEMS

Problem 1:

Charlie worked for a stone setting company this past summer. He earned $50 just for coming to work and an additional $30 every hour for each hour he worked. The linear function E(t) = 50 + 30t represents Charlie’s earnings E as a function of time worked t (in hours).

a)  Explain what E(4) represents.

b)  Find E(8). Explain what this represents in this problem.

c) Find E(5) - E(2).

Explain what this represents in this problem.

Solution :

Given, E(t) = 50 + 30t

a)  E(4) = 50 + 30 × 4

E(4) = 50 + 120

E(4) = 170

E(4) represents the money earned by Charlie working for 4 hours. He is earning $170 for 4 hours.

b) E(8) = 50 + 30 × 8

E(8) = 50 + 240

E(8) = 290

Charlie earning $290 after working for 8 hours at stone cutting company.

c) 

E(5) - E(2) = 200 - 110

E(5) - E(2) = 90

Problem 2 :

Kristen has $500 in her savings account. She is able to save $50 each month. The function S(m) = 50m + 500 represents the amount of money in her savings account S as a function of time in months m.

a) Find S(2). Explain what this represents in this problem.

b) Find m such that S(m)=800. Explain what this represents in this problem.

Solution :

Given, S(m) = 50m + 500

a) S(2) = 50(2) + 500

S(2) = 100 + 500

S(2) = 600

S(2) represents the amount of money in her saving accounts in 2 months.

b)

S(m) = 800

800 = 50m + 500

50m = 800 - 500

50m = 300

m = 6

After 6 months, he will have 800.

Problem 3 :

Luke is driving home from work. Let D(t) denote Luke’s remaining distance to drive D (measured in miles) after t minutes of driving.

What does the statement D(0) = 10 mean?

a) The drive between Luke’s home and his workplace takes 10 minutes.

b) The drive between Luke’s home and his workplace is 10 miles long.

c) Luke’s remaining distance is 0 miles after 10 minutes.

Solution :

D(0) = 10

Comparing D(0) with D(t), we understand that the meaning of t is time. When t = 0 means he didn't start travelling.

So, 

the drive between Luke’s home and his workplace is 10 miles long.

Problem 4 :

Ryan’s class had a math quiz where the grades were between 0 and 10. Let N(g) denote the number of students N whose grade on the exam was g.

What does the statement N(K) = 8 mean?

a) There are 8 students whose grade on the exam was K.

b) The value of the unknown K is equal to 8.

c) There are K students whose grade on the exam was 8.

Solution :

There are 8 students whose grade on the exam was K.

Statement (a) is correct.

Problem 5 :

Alicia went for a walk. Let D(t) denote the distance Alicia walked D (measures in miles) after walking for t hours.

What does the statement D(0.5) < D(1) - D(0.5) mean?

a) The distance Alicia has walked after walking for an hour is greater than the distance she has walked after half an hour.

b) The time it took Alicia to walk the first half mile is shorter than the time it took her to walk the following half mile.

c) The distance Alicia walked during the first half hour is shorter than the distance she walked during the following half hour.

Solution :

The distance Alicia walked during the first half hour is shorter than the distance she walked during the following half hour.

Statement (c) is correct.