F(x) = bx and g(x) = logb x are inverse functions. Explain why each of the following are true

1. A translation of function f is f1(x) = b(x – h). It is equivalent to a vertical stretch or vertical compression of function f.

2. The inverse of f1(x) = b(x – h) is equivalent to a translation ofg.

3. The inverse of f1(x) = b(x – h) is not equivalent to a vertical stretch or vertical compression of g.

4. The function h(x) = logc x is a vertical stretch or compression of g or of its reflection –g. Read this as “negative g”.

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