The diagrams A, B, C, D, E and F show six graphs of different functions.

  1. (a)

    yy is inversely proportional to xx,

    Diagram ...

  2. (b)

    y=xny = x^n, where nn is an odd integer greater than 1,

    Diagram ...

  3. (c)

    y=nxy = n^x, where nn is an integer greater than 1.

    Diagram ...

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Worked solution

6(a)

1. Identify the graph shape for inverse proportionality and match it to the diagram

If yy is inversely proportional to xx, then
y=kx.y=\frac{k}{x}.
For positive kk and x>0x>0, the graph is a decreasing reciprocal curve in the first quadrant, approaching both axes. This matches Diagram C.

Answer

Diagram C

6(b)

1. Identify the graph shape for $y=x^n$ with odd $n>1$ and match it to the diagram

For y=xny=x^n, where nn is an odd integer greater than 11, the graph is an increasing S-shaped curve passing through the origin, with negative yy-values for negative xx and positive yy-values for positive xx.

This matches Diagram E.

Answer

Diagram E

6(c)

1. Identify and match the exponential graph shape

For y=nxy=n^x where n>1n>1, the graph is an increasing exponential curve with y>0y>0 for all xx, and it becomes steeper as xx increases.

This matches Diagram B.

Answer

Diagram B

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