Figure 1 shows a sketch of the curve with equation y = \frac{3}{x}, \ x \neq 0. (a) On a separate diagram, sketch the curve with equation y = \frac{3}{x + 2}, \ x \neq -2, showing the coordinates of any point at which the curve crosses a coordinate axis. (b) Write down the equations of the asymptotes of the curve in part (a).

A-Level Edexcel Maths Pure Quadratics: Figure 1 shows a sketch of the c

Figure 1 shows a sketch of the curve with equation y = \frac{3}{x}, \ x \neq 0 - Edexcel - A-Level Maths Pure - Question 7 - 2007 - Paper 1

Question 7

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Figure 1 shows a sketch of the curve with equation y = \frac{3}{x}, \ x \neq 0. (a) On a separate diagram, sketch the curve with equation y = \frac{3}{x + 2},... show full transcript

Worked Solution & Example Answer:Figure 1 shows a sketch of the curve with equation y = \frac{3}{x}, \ x \neq 0 - Edexcel - A-Level Maths Pure - Question 7 - 2007 - Paper 1

Step 1

Sketch the curve with equation y = \frac{3}{x + 2}

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Answer

To sketch the curve, start by identifying the transformations from the original function (y = \frac{3}{x}). This equation translates the graph to the left by 2 units. Thus, all points will be shifted left, changing the x-intercept accordingly.

1. Identifying Intercepts

Find x-intercept: Set (y = 0) which is impossible for this equation; hence no x-intercept exists.
Find y-intercept: Set (x = 0):
[ y = \frac{3}{0 + 2} = \frac{3}{2} ]
So the y-intercept is at ((0, \frac{3}{2})).

2. Drawing the Curve

The graph will have two branches, with the left branch approaching the vertical asymptote at (x = -2) and heading towards infinity, while the right branch also approaches this asymptote but from above.
The sketch should show these branches and the point at the y-intercept as described.

3. Marking the Diagram

Mark the y-intercept at ((0, \frac{3}{2})) clearly on the diagram.

Step 2

Write down the equations of the asymptotes of the curve in part (a)

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