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The diagram shows the graph of the function $f(x) = ext{log}_2 x$, where $x > 0$ - Scottish Highers Maths - Question 9 - 2023

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Question 9

The-diagram-shows-the-graph-of-the-function-$f(x)-=--ext{log}_2-x$,-where-$x->-0$-Scottish Highers Maths-Question 9-2023.png

The diagram shows the graph of the function $f(x) = ext{log}_2 x$, where $x > 0$. The inverse function, $f^{-1}$, exists. On the diagram in your answer booklet, sk... show full transcript

Worked Solution & Example Answer:The diagram shows the graph of the function $f(x) = ext{log}_2 x$, where $x > 0$ - Scottish Highers Maths - Question 9 - 2023

Step 1

Final adjustments to the graph

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Answer

In summary, when sketching this graph, maintain the characteristics:

  • The graph should remain concave up above the x-axis for x>0x > 0.
  • It must pass through (0,0)(0, 0) and (1,1)(1, 1),
  • As xx approaches negative infinity, the curve approaches y=1y = -1.
  • Be mindful of ensuring a smooth curve without sharp corners as per typical behavior of exponential graphs.

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