Question

If the function f(x) has a domain of `-2<=x<= 8` and a range of `-4<= y <= 6` and the function g (x) is defined by the formula `g(x)=5f(2x))` then what are the domain and range of g?

Answer 1

Below.

Explanation:

Use basic function transformations to find the new domain and range. `5f(x)` means that the function is vertically stretched by a factor of five.

Therefore, the new range will span an interval that is five times greater than the original. In the case of `f(2x)`, a horizontal stretch by a factor of a half is applied to the function. Therefore the extremities of the domain are halved.

Et voilà!