Can a linear function be continuous but not have a domain and range of all real numbers?

Question

misty1212 · Answer

HI!!

misty1212 · Answer

sure why not?

misty1212 · Answer

first of all, the domain of a function is something the creator of the function controls, so you can say the domain is anything you like
this is not the answer they are looking for however

misty1212 · Answer

the answer they are looking for is an example of a linear function whose domain is $\mathbb{R}$ but whose range is not
hint, what linear function has only one range element?

amberlykhan · Answer

idk im confused cuz i just started this topic

misty1212 · Answer

a linear function looks like $$f(x)=mx+b$$a  line with slope $m$ and $y$-intercept $b$

amberlykhan · Answer

i wrote that its yes because as long as the domain doesnt repeat it can be anything

misty1212 · Answer

if $m=0$ then you get $f(x)=b$ a constant function 
the domain  is still all real numbers, but the range is only one number 
the line is horizontal

amberlykhan · Answer

but doesnt it say that the domain and range cant be real numbers?

amberlykhan · Answer

@misty1212