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Understanding Functions: Domain, Range, and Relations in Mathematics

This guide covers essential concepts in determining functions, expressing relations as ordered pairs, and exploring domains and ranges. It includes methods for evaluating functions, such as finding specific outputs and expressing variables in equations. Practical examples illustrate real-life applications, such as cost calculations in a car hire scenario and burger pricing equations. Additionally, the significance of graphs and mapping diagrams in representing mathematical functions is highlighted.

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Understanding Functions: Domain, Range, and Relations in Mathematics

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  1. 1 Determine if the following are functions no yes

  2. 2 State domain and range of the function below: D: (-, ) R: [-1, ) (1, -1)

  3. 3 Write the relation shown in the mapping as a set of ordered pairs. {(0, 6), (1, 1), (-4, 0), (4, 1)}

  4. 4 State domain and range of the function below: D: [0, 3] R: [-6, 5]

  5. 5 Determine whether this relation is a function. Then state the domain and range. {(1, 4), (2, 3), (3, -6), (-3, 6)} Yes, it’s a function D: {-3, 1, 2, 3} R: {-6, 3, 4, 6}

  6. 6 Given that Find: a) f(-3) b) f(x + 2) = 3 = x2 + 6x + 8

  7. 7 Given that f(x) = 2x -10 = -4 a) evaluate: f(3) b) solve f(x) = 32 x= 21

  8. 8 y x Express as amapping for the domain {-1, 0, 1, 2, 3}. -1 0 1 2 3 -3 -2 1 6

  9. 9 Represent the function y = 2x2 – 5, where xis an element of {–2, –1, 0, 1, 2, 3} by a mapping diagram. y x -2 -1 0 1 2 3 -5 -3 3 13

  10. 10 Write the relation shown in the mapping as a set of ordered pairs. {(4, 3, )(4, 8), (1, 7), (-8, 1), (2, 1), (2, 3)}

  11. 11 For a small car hire company charges €22 per day plus 13 cents for each kilometer , d, driven. • (a) Find the total cost, C, of hiring a car for a day if you travel • (i) 50km • (ii) 300km. • Find the equation connection the variables. • (c) Using your equation find how many kilometers you traveled if your bill was €47. € 28.50 € 61 C = 22 + 0.13d 192.31 km

  12. 12 At Jumbo’s Burger Bar, Jumbo burgers cost £J each and regular cokes cost £C each. Two Jumbo burgers and three regular cokes cost £5.95. Write an equation to show this. (b) If one Jumbo Burger costs £2.15, what is the cost, in pence, of one regular coke? 2J + 3C = 5.95 55 pence

  13. 13 Are the following graphs functions? yes no

  14. 14 State the Domain and Range {(-5,0) , (3,0) , (14, 1) , (2006, 1)} D: {-5, 3, 14, 2006} R: {0, 1}

  15. 15 Are the following functions? T={(-1,1), (2,1), (4,-1), (5,2) A={(a,c), (b,d), (e,f), (a,h)} yes no

  16. 16 y x Express the data below as a graph and a mapping -2 -1 1 3 -4 -2 -1 1 4

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