Suppose that f(x) has a domain of [4,18] and a range of [2,12]. What are the domain and range of:a) f(2 x) b) 2 f(x)

Question

How do you find the domain and the range?

Answer 1

the domain is what the input numbers can be. normally this is just the x, but if the function "does something" to the x  then the domain becomes what the "something" did to the x.

In your problem: the x can be anything from 4 to 18;

so the domain of f(2x) is anything from 2 * 4 to 2 * 18 or 8 to 36

 

 

Range- this is what the output values can be it or the Y values on a graph. Normally this is the f(x) but doing "something" to the f(x) means Y changes to so the range will be as well.

In your problem the range of f(x) is anything from 2 to 12.

so the range of 2f(x) will be anything from 2 * 2  to 2 * 12  or from 4 to 24

Answer 2

Randy is correct.  I'd like to add however that you also would like to consider if you can say anything about the  range on f(2x).  Think about it, do we really know what the orginal function f(x) was spitting out?  Was it a line, a quadratic, or something even more complicated?

Does doubling the input affect the output that you can get?  Are the ends bound no matter what we put in, can you even know?  We really can't say a lot about the range here.

Then for 2*f(x), we have doubled all the outputs (range), but we haven't changed what we are allowed to put in, so have you done anything at all to the domain?

So, we can say something about both the domain and range of 2*f(x) probably.  But, we likely can't say the same for f(2x) without more information.