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# Sam maths pres

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### Sam maths pres

1. 1. Transforming Graphs<br />Year 12 Mathematical Methods<br />Sam Roberts<br />
2. 2. Graphing transformations of the graph of f(x)=logax<br />Dilation on the x-axis is shown by the number at the front of the equation. E.g. f(x)=3loga x<br />Dilation on the y-axis is shown by the number in front of the pronumeral. E.g. f(x0=loga 2x<br />
3. 3. Graphing transformations of the graph of f(x)=logax<br />Translations on the x-axis is shown by the number added or subtracted to x. E.g. f(x)=loga (x-5)<br />Translation on the y-axis is shown by the number at the end of the equation. E.g. f(x0=loga x +5<br />
4. 4. Graphing transformations of the graph of f(x)=logax<br />Reflection on the x-axis is shown by the symbol at the front of the equation. E.g. <br />f(x)=-loga x<br />Reflection on the y-axis is shown by dividing the equation to 1. E.g. f(x)= 1 _loga x<br />
5. 5. Graphing circular function transformations<br />
6. 6. Finding the degrees when the result is in radians. Vice Versa.<br />Eg3π x 180 = 540 = 135°<br /> 4 π 4<br />Eg 30° x π = 30π = π<br /> 180 180 6<br />
7. 7. Exact Values Triangles<br />
8. 8. Finding axis intercepts<br />Let y = 0 to find x intercepts<br />
9. 9. Finding the inverse of log equations<br />Sub x as y to find the inverse<br />Logaaˣ=x for all x Є R<br />logax<br />a =x for x Є R<br />
10. 10. Finding a rule for f∘g(x)<br />Sub the equation of g(x) where the x in f(x) equation<br />Eg. g(x)=ǀxǀ and f(x)<br />f∘g(x)=sin(ǀxǀ)<br />