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?

1 Answer
Feb 13, 2018

Answer:

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.

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Et voilà!