1. Transforming Graphs Year 12 Mathematical Methods Sam Roberts

2. Graphing transformations of the graph of f(x)=logax Dilation on the x-axis is shown by the number at the front of the equation. E.g. f(x)=3loga x Dilation on the y-axis is shown by the number in front of the pronumeral. E.g. f(x0=loga 2x

3. Graphing transformations of the graph of f(x)=logax Translations on the x-axis is shown by the number added or subtracted to x. E.g. f(x)=loga (x-5) Translation on the y-axis is shown by the number at the end of the equation. E.g. f(x0=loga x +5

4. Graphing transformations of the graph of f(x)=logax Reflection on the x-axis is shown by the symbol at the front of the equation. E.g. f(x)=-loga x Reflection on the y-axis is shown by dividing the equation to 1. E.g. f(x)= 1 _loga x

5. Graphing circular function transformations

6. Finding the degrees when the result is in radians. Vice Versa. Eg3π x 180 = 540 = 135° 4 π 4 Eg 30° x π = 30π = π 180 180 6

7. Exact Values Triangles

8. Finding axis intercepts Let y = 0 to find x intercepts

9. Finding the inverse of log equations Sub x as y to find the inverse Logaaˣ=x for all x Є R logax a =x for x Є R

10. Finding a rule for f∘g(x) Sub the equation of g(x) where the x in f(x) equation Eg. g(x)=ǀxǀ and f(x) f∘g(x)=sin(ǀxǀ)