Computational Mathmatics

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ITSU2011

Computational Mathematics

Activity 06

Victorian Institute of Technology Pty Ltd

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Use the graph plotting website (https://www.desmos.com/calculator) where applicable to

determine if the relation is a function or not.

Part A)

Part B)

1) The function f is defined as 𝑓(𝑥) = √𝑥 − 3. Its domain is 𝑥 ≥ 3, and its range is 𝑓(𝑥) ≥

0. Which of the following is true of f?

A. If x ≥ 3, then f(x) ≥ 0.

B. It assigns exactly one value to every positive value of x.

C. The range of the function is f(3).

D. The value of f(3) is undefined.

2. If g(x) = 3x + x + 5, evaluate g(2).

A. g(2) = 8

B. g(2) = 9

C. g(2) = 13

D. g(2) = 17

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3. The function 𝑆(𝑟) = 4 𝑟𝜋 2 gives the surface area of a sphere of radius r. What is the surface

area of a sphere of radius 4?

A. 8 π

B. 16π

C. 32π

D. 64 π

4. A theatre will sell 500 tickets to a play if it charges $10 per ticket. Furthermore, every time it

raises the price by one dollar, it will sell 50 fewer tickets because some people will think it too

expensive. Which of the following functions t(d) represents the number of tickets the theater will

sell if it charges d dollars per ticket?

A. t(d) = 50d + 10

B. t(d) = 50d + 1000

C. t(d) = 50d

D. t(d) = 50d + 10

5. A taxi ride costs $4.25 for the first mile and $0.70 for each mile after the first. Which of the

following functions c(d) gives the total cost (in dollars) of traveling d miles (assuming that d ≥

1)?

A. c(d) = 3.55 + 0.70d

B. c(d) = 3.55 + 0.70(d – 1)

C. c(d) = 4.25 + 0.70d

D. c(d) = 4.25 + 0.70(d – 1)

6. Exponential functions grow by equal factors over equal intervals. By what factor does the

exponential function f(x)=3-2x grow by over every interval whose length is 3?

A. By a factor of 6

B. By a factor of 8

C. By a factor of 18

D. By a factor of 24

7. A linear function can be used to convert a temperature from Fahrenheit to Celsius. For

example, you can use it to convert 32oF to 0o C and 68o F to 20oC. Use this information to

convert 104o F to Celsius.

A. 25o C

B. 30o C

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C. 40 oC

D. 50o C

Part C

1. Is g (x) = x² - 2 an onto function where 𝑔: 𝑅 → 𝑅?

2. Is g (x) = x² - 2 an onto function where 𝑔: → [−2, ∞)?

3. Check the surjectivity of 𝑓: 𝑍 → 𝑍 given by 𝑓(𝑥) = 𝑥2, where 𝑍 is a set of real integers.

4.