Given f(x) = ln(x) & the transformations below, write the equation g(x) for the transformed function.

Question

1. Vertical shift up 2 units
2. Horizontal shift right 3 units
3. Vertical stretch of 5 units
4. Reflected across the x-axis.

Answer 1

vertical shift up 2: ln(x) + 2

horizontal shift right 3: ln(x-3) + 2

vertical stretch of 5: 5ln(x-3) + 2

reflect across x-axis: -5ln(x-3) + 2 (this is g(x))

Check it out--do the above steps one at a time to see the transformations happening.

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