How to sketch both cartesian and parametric graphs on the same diagram using GC

Example 1

DHS J1 2018 Aug Test

DHS 2018 J1 Aug test

Suppose we want to sketch the curve C and the line y=-2x+2 on the same graph

DHS 1

Note how the line y-2x+2 is entered.DHS 2

Adjust the Tmax to 1%  more so the graph displays correctly.DHS 3

Example 2

2011 alevel P1 Q11

2011 alevel P1 Q112011 GC12011 GC2

Finding sequence of transformation

Usually the sequence of transformation can be found by the replacement method. However, it can be tough to find the replacement for complicated functions. For such cases, we can use the general linear transformation c f(bx+a)+d to find the sequence.

cf(bx+a)+d = Translate by a units in the negative X direction, then scale by a factor of 1/b parallel to the X-axis, then scale by a factor of c parallel to the Y-axis, then translate by d units in the positive Y direction.

Example

NYJC 2016 prelim

Solution

NYJC 2016. alterativeJPG

Square root graph: ‘Pointed’ or ‘Rounded’ at X-intercept (9740 syllabus only)

Square root graph can appear as ‘Pointed’ or ‘Rounded’ at the X-intercept.

The shape depends whether the original point on X-axis is a stationary point.

square root theory

Example 1

sq1

2

x=-3 is a stationary point. Therefore, the square root graph at x=-3 will be pointed.

x= 2 is not a stationary point. Therefore, the square root graph at x= 2 will be rounded.

Example 2

ex2

To determine the shape of the square root graph at the x-intercept, we can use GC to determine the gradient.

1

Therefore, the first graph at x=1 appears as two oblique tangents while the second graph at x=1 is flat.

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