Supposed that f(x) has a domain of [10,18] and a range of [7,15]. What are the domains and ranges for the following? (a) f(2x) (b) 2f(x)

Answer 1

So when we are looking at domain, we're looking at inputs, which are your x-values, and when we're looking at range, we're looking at your outputs, or y-values.

(You might/probably already know that.)

Great. So what does that have to do with f(2x) and 2f(x)?

If the factor changes within our function f(2x), it's going to change our domain. Strangely enough, it's actually going to change them by a factor of 1/2 and not 2. Our domain was [10,18] so if we have f(2x), our domain becomes [5,9].

Now let's look at 2f(x). This changes our range. This one is more intuitive: my range multiplies by a factor of 2. It was [7,15], now it is [14,30].

Hope this helps! Graph transformations with unknown functions are tricky.