How do you describe graph translations on x and y?
On the y-axis: if the graph is moved vertically up by 'n', its affecting the y value by a positive amount, so your (x,y) becomes (x,y+n) and your equation becomes y+n=f(x) rather than y=f(x), or equally becomes y=f(x)-n by rearranging the equationOn the x-axis: if the graph is moved horizontally to the right, so again by a positive amount 'n', your (x,y) becomes (x+n,y) as this time it's affecting the x value. The equation becomes y=f(x-n) rather than y=f(x).The best way to understand these is by playing around and drawing some graphs, then putting the numbers into the equations and working them backwards - draw out examples of this with the student. But a way to remember the basis for the exam, is simply, if your graph is moved by a positive amount n, in either the x or y direction, then you add this n on to the co-ordinate value its affecting. For the equations, if it affects x you will get y=f(x-n) and in y, y=f(x)-n. So by being moved a positive amount n, this n is added to the co-ordinated, and minused from the equations if y alone is the subject. Tutoring points:patience, it may take the student a few times over to get this as it can be complicated and confusing to a lot of students, but it just takes time, practise and encouragment to play around with graphs student needs to understand that an equation can be expressed by y= or f(x)=student needs to know intial basic graphs such as x, x2, ln(x) etc, this will depend on their specification this needs to be taught drawing each graph out!needs to be taught with equations so student understands having the f(x) and how to use this in exams
