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The curve $$y = ext{log}_4 x$$ is transformed by a stretch, scale factor 2, parallel to the y-axis - AQA - A-Level Maths Pure - Question 3 - 2022 - Paper 1

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The curve $$y = ext{log}_4 x$$ is transformed by a stretch, scale factor 2, parallel to the y-axis. State the equation of the curve after it has been transformed... show full transcript

Worked Solution & Example Answer:The curve $$y = ext{log}_4 x$$ is transformed by a stretch, scale factor 2, parallel to the y-axis - AQA - A-Level Maths Pure - Question 3 - 2022 - Paper 1

Step 1

State the equation of the curve after it has been transformed.

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Answer

The transformation described is a vertical stretch by a factor of 2, which affects the logarithmic function. Therefore, the transformed equation can be expressed as:

y=2extlog4xy = 2 ext{log}_4 x

This means that for every value of xx, the output of the log function is doubled.

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