Question

How do you find the domain and range of a function?

How do you find the domain and range of a function algebraically without a graph? Please don't give me an easy example and solve it. Instead what method should I use to get a reliable answer every time?

My textbook finds it out using graphs. But no calculators are allowed at all in the exam, and I wouldn't really have the time to plot difficult ones anyway. Any help would be appreciated.

Answer 1

domain = what x values can exist
range = what y values can exist

Answer 2

if you give me an equation that you want worked out i wll do so for you

Answer 3

Ok here we go \[\sqrt{-x^2 - x + 6}\]

Answer 4

I have solved the quadratic equation for 0, and I have gotten the answers as x = -3, 2
So that means that that is the domain, correct?

Answer 5

ok so the rules for continuity come into play
1) no division by zero univers will implode
2) no log or LN <1
3) no sqrt of -#

Answer 6

yes that is the domain

Answer 7

The answer for the question in the textbook says that "Domain: {−2 ≤ −x ≤ 3}, Range: {0 ≤ g(x) ≤ 5/2}."

Answer 8

sorry my postwaswrong for the range, im a bit sleepy

Answer 9

Where are they getting the range of 0 and 2.5 though?

Answer 10

sketchingthe graph is the most reliable way to check it. even if you just plot oints you can see where this function exists.

Answer 11

So just quickly put in a few x values to get a rough sketch and approximate using that?

Answer 12

yep thats the easiest way. most functions youwill just recognize very quickly the only ones you really have to lok at are those with very restrictive x values