# Category: Graphing and Transformation

## How to graph X given Y

Example 1: Volume of revolution in 2017 alevel P2 4b

Let a=2 so we can visualise the shape of the graph

Example 2: Solution curve for Differential equation. 2014 alevel P1

This is solution for part iv.

It can be sketched without expressing the solution in the form x=f(t)

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

**Example 1**

DHS J1 2018 Aug Test

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

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

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

**Example 2**

2011 alevel P1 Q11

## 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**

**Solution**

## Sketching Periodic functions with GC

Suppose we want to sketch the graph from -3 to 8.

- Enter by pressing “Math, Piecewise”.

2. Adjust the window setting to the required domain.

3. Trace the end point at -3 since it is not 1 complete cycle.

## How to check Sequence of Transformation?

## Advanced graph transformation

Advanced graph transformation can be done in stages, using the replacement method. Each time, we replace x or y.

## Challenging graphing technique question 1

This question was posted by a student at Singapore JC maths.

**Solution for Part ii**

## 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.

Example 1

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**

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

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