Please have a go at sketching the core graph shapes we have come across so far in AS and the beginning of A2 on your own

Can you check your partners and discuss any differences Can you check your partners and discuss any differences. If you can’t settle your disagreements ask the others on your table or me

If f(x) = sin x sketch the graph of 2f(x) with x axis in radians 13/01/2019

If f(x) = cos x sketch the graph of f(3x) with the x axis in degrees 13/01/2019

If f(x) = 1/x sketch the graph of f(x)+5 13/01/2019

If f(x) = lnx sketch the graph of f(x-4) 13/01/2019

If f(x) = (x-3)(x+4) sketch the graph of -f(x) 13/01/2019

If f(x) = (x-2)2(x+4) sketch the graph of f(-x) 13/01/2019

Transforming Graphs of Functions As a summary of the rules from AS maths f(x + a) is a … f(x) + a is a … f(ax) is a … af(x) is a … -f(x) is a … f(-x) is a … Translation of –a units in the x direction Translation of a units in the y direction Stretch in the x direction of scale factor 1/a Stretch in the y direction of scale factor a Reflection in the x-axis Reflection in the y-axis 5D

Using the big boards, as a table, can you try and sketch y = 4e2x + 3

Transforming Graphs of Functions y = (x – 2)2 + 3 y = (x – 2)2 y = x2 You need to be able to apply multiple transformations to the same curve Sketch the graph of:  Build the equation up from y = x2 7 Translation, 2 units right Translation, 3 units up

Transforming Graphs of Functions y = 2/x + 5 You need to be able to apply multiple transformations to the same curve Sketch the graph of:  Build the equation up from y = 1/x y = 1/x + 5 y = 1/x 2/5 Translation, 5 units left Stretch in the y direction, scale factor 2 5D

Transforming Graphs of Functions You need to be able to apply multiple transformations to the same curve Sketch the graph of:  Build the equation up from y = cosx 2 y = cos2x 1 y = cosx 90 180 270 360 -1 -2 y = cos2x - 1 Stretch in the x direction, scale factor 1/2 Translation 1 unit down 5D

Transforming Graphs of Functions You need to be able to apply multiple transformations to the same curve Sketch the graph of:  Build the equation up from y = x - 1 y = 3|x – 1| y = x - 1 3 y = |x – 1| 1 1/3 1 1 5/3 y = 3|x – 1| - 2 -1 Reflect negative values in the x-axis Stretch in the y direction, scale factor 3 You will need to do more than one sketch for these – do not do lots on the same diagram! Translation 2 units down 5D

Using the big boards again can you check and correct the graphs you sketched earlier of y = 4e2x + 3 Showing the correct steps to build up the graph

Exercise 5D

Transforming Graphs of Functions B(6,8) B(6,7) When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates To the right is the graph of y = f(x) Sketch the graph of: y = 2f(x) – 1 and state the new coordinates of O, A and B… B(6,4) O O(0,-1) A(2,-1) y = f(x) A(2,-2) A(2,-3) y = 2f(x) y = 2f(x) - 1 Vertical Stretch, scale factor 2  y-values double Vertical translation 1 unit down  y-values reduced by 1 5E

Transforming Graphs of Functions y = f(x + 2) + 2 B(4,6) When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates To the right is the graph of y = f(x) Sketch the graph of: y = f(x + 2) + 2 and state the new coordinates of O, A and B… B(6,4) B(4,4) A(0,1) O(-2,2) O(-2,0) O A(0,-1) A(2,-1) y = f(x) y = f(x + 2) Horizontal translation 2 units left  x-values reduced by 2 Vertical translation 2 units up  y-values increased by 2 5E

Transforming Graphs of Functions y = 1/4f(2x) When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates To the right is the graph of y = f(x) Sketch the graph of: y = 1/4f(2x) and state the new coordinates of O, A and B… B(3,4) B(6,4) B(3,1) A(1,-0.25) O A(1,-1) A(2,-1) y = f(x) y = f(2x) Horizontal stretch, scale factor 1/2  x-values divided by 2 Vertical stretch, scale factor 1/4  y-values divided by 4 5E

Transforming Graphs of Functions y = f(x - 1) When you are given a sketch of y = f(x), you need to be able to sketch transformations and show the final position of original co-ordinates To the right is the graph of y = f(x) Sketch the graph of: y = -f(x - 1) and state the new coordinates of O, A and B… B(6,4) B(7,4) A(3,1) O(1,0) O A(2,-1) A(3,-1) y = f(x) B(7,-4) y = -f(x - 1) Horizontal translation 1 unit right  x-values increase by 1 Reflection in the x-axis  y-values ‘swap sign’ (times -1) 5E

Exercise 5E and Exercise 5F

Assignment 3 for 1 week today