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P2 functions and equations from a graph questions

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P2 functions and equations from a graph questions

1. 1. UNIT 18 COMPUTATIONAL THINKING P2; identify linear and quadratic functions obtain the equation of a straight line from a graph
2. 2. Functions What are they? • Why are they useful to us in Computing?
3. 3. Functions What are they? “Functions are a relation or expression involving one or more variables” i.e They are a way of writing down a problem or sum when you don’t know all the figures or answers. e.g.
4. 4. Functions Why are functions useful to us in Computing? They help us keep clear what we know and don’t know. They help us write problems in a way that start to help us work out the answer
5. 5. Functions What are they? “Functions are a relation or expression involving one or more variables” i.e They are a way of writing down a problem or sum when you don’t know all the figures or answers. e.g. here is a simple sum to help us do harder ones later Two students bought 10 cans of coke If one student bought 4 cans, how many were bought by the other student? We would write it like this; 10 cans bought = (1 * 4 cans) + (1 * x cans) 10 = 4 + x or we can write; x + 4 = 10 (to get the one thing we need to know (x) on the left) (Rule to Remember if we move a number to the opposite side we have to change the sign plus (+) becomes minus (-) and times (x) becomes divide (÷) ) x = 10 – 4 x = 6 so the other student bought 6 cans
6. 6. Functions Exercise Two lecturers bought 10 pens If one lecturer bought 4 pens, how many were bought by the lecturer? Write out your working; ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. Answer: The other lecturer bought …… pens
7. 7. Functions It’s your birthday and you are buying cakes for all your group You decide to buy bakewell tarts which come in boxes of 6. You have 18 in your group How many boxe do you need to buy? We would write it like this; No of boxes multiplied by 6 per box = 18 tarts (at least) x * 6 = 18 (we need to know (x) on the left on its own) (Rule to Remember if we move a number to the opposite side we have to change the sign plus (+) becomes minus (-) and times (x) becomes divide (÷) ) x = 18 ÷ 6 x = 18/6 x = 3 Answer: I need to buy 3 boxes
8. 8. Functions Exercise It’s your birthday and you are buying cakes for all your friends You decide to buy bakewell tarts which come in boxes of 6. You have 30 friends How many boxes do you need to buy? Write out your working; ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. ………………………………………………………………………………….. Answer: I need to buy …….. boxes
9. 9. Functions Exercise Write out the answers What are functions? ………………………………………………………………………………….. ………………………………………………………………………………….. Why are they useful to us in Computing? ………………………………………………………………………………….. …………………………………………………………………………………..
10. 10. Graphs – x and y axis x y Graphs let us see figures in a graphical way and help us understand them more easily. • There is an x and a y axis marked with their values • Usually only the top right hand corner with positive values of x and y is shown
11. 11. Graphs – x and y axis x y Remember the game ‘Battleships’ ? Battleships have a location based on columns and rows named by letters and numbers – called coordinates. Eg B7 and A3 Graphs have points with coordinates eg (2,4) (where x=2 and y=4) • If x = 2 then location of the point is somewhere on the red line • If y = 4 then location of the point is somewhere on the blue line If x = 2 and y = 4 then location of the point is exactly where the red line and the blue line cross (or intersect)
12. 12. Gradients - uphill x y A GRADIENT IS: Rise over Run i.e. distance up ÷ distance along 1 ÷ 7 = 1 in 7 Gradient = 1 in 7 or 0.143 or 14.3% What is the gradient?
13. 13. Gradients - downhill x y A GRADIENT IS: Rise over Run i.e. distance up ÷ distance along 1 ÷ 7 = 1 in 7 Gradient = 1 in 7 or -0.143 or 14.3% This is easier for whole numbers but what if the numbers are decimals What is the gradient?
14. 14. Gradients - if you don’t know the distances x y A GRADIENT IS: Rise over Run i.e. distance up/down ÷ distance along – but if you only have coordinates; Take the coordinates (x1,y1) of a point on a line graph eg 1,1 Take the coordinates (x2,y2) of another point on a graph eg 3,3 y2 - y1 3-1 2 1 Gradient = ------ = --------- = ------- = ---------- = +1 x2 - x1 3-1 2 1 What is the gradient?
15. 15. Getting equations from a straight line graph x y x = 0 1 2 3 4 5 6 M*x= +C= y = Therefore the equation for this graph is: y = What is the equation? A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = 1 C is where it crosses over = 0
16. 16. Getting the equation from a graph 1 x y Therefore the equation for this graph is: y = ………………………….. What is the equation? x 0 1 2 3 4 5 6 Mx +C y = A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = 1 C is where it crosses over = 1
17. 17. Getting the equation from a graph 2 x y x 0 1 2 3 4 5 6 Mx +C y = Therefore the equation for this graph is: y = ………………………….. A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = 1 C is where it crosses over = 2 What is the equation?
18. 18. Getting the equations from graphs 3 + 4 x y x 0 1 2 3 4 5 6 Mx 1*0 1*1 1*2 1*3 1*4 1*5 1*6 +C y = The equation for the Red graph is: y = (1 * x) + …. or y = x + …. The equation for the Blue graph is: y = (1 * x) + …. or y = x + …. A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = 1 C is where it crosses over = ? What is the equation for the red and blue graphs?
19. 19. Getting the equation from a graph 5 x y x 0 1 2 3 4 5 6 Mx +C y = Therefore the equation for this graph is: y = ………………………….. A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = -1 C is where it crosses over = 0 What is the equation?
20. 20. Getting the equation from a graph 6 x y x 0 1 2 3 4 5 6 Mx +C y = Therefore the equation for this graph is: y = ………………………….. A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = -1 C is where it crosses over = 2 What is the equation?
21. 21. Getting the equation from a graph 7 x y x 0 1 2 3 4 5 6 Mx +C y = Therefore the equation for this graph is: y = ………………………….. A STRAIGHT LINE GRAPH EQUATION IS ALWAYS: y = Mx + C Where M = gradient = ………..? C where it crosses over = …..? What is the equation?
22. 22. Well Done! You have used functions You have worked out the equation for a straight line graph