#Determining domain and range
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,rotate
So what is your question. You have posted 3 different questions
Like what’s the process in deterring the domain and range
The working out
Where do you start
Something that I usually do is that I:
- Look at the type of function that I'm dealing with. Depending on whether or not x can be negative or a specific value or depending on the exists of asymptotes, my answers are gonna change.
- I look for possible restrictions. It is directly linked to 1) but it is more applied. I look if there is a possible division by 0 somewhere, if the x-value is negative why it shouldn't, etc.
- I look for horizontal and vertical translations. If you have a basic idea of how your general function works without transformation, you can just use the mapping rule on the domain and range:
(e.g.: sqrt(x), D: (0, +∞), R: (0, +∞))
(sqrt(x+1) : (0-1, +∞-1) = (-1, +∞))