Question

Write a logarithmic function that represents the following transformations applied to the parent function: Reflection over the y-axis, a vertical stretch by a factor of (5/3) a transformation right 2 units, and a transformation down 6 units.

Answer 1

Original function;

y = logbX

Transformation;

y = -5/3logb(x + 2) - 6

Explanation:

General form of a logarithmic function is given below;

y = logb X (log to base b)

Reflection over the y-axis

y value remains same, x becomes negative

y = - logb X

Vertical stretch by a factor of 5/3

This means that we multiply the whole function by 5/3

That will be;

y = -5/3logbX

Transformation right 2 units

This means that we add the value of 2 to the x-axis value

y = -5/3logb(x + 2)

transformation down 6 units

This means that we subtract 6 from the total y value

y = -5/3logb(x + 2) - 6