Ok i have an exam tomorrow, and looking over the past papers I dont understand what it means for one particular question.
Question - For each of the following functions determine the largest possible DOMAIN and corresponding RANGE.
1. f(x) = 3x + 2
2. g(x) = X^2 + 1
3. h(x) = 1/(3x+2)
4. k(x) = 1/(x^2 + 1)
x^2 means squared by the way.
I know the domain is the x value and the range is the y value, but i'm just not sure what im meant to be doing.
Help?
I'll try to explain for ya...
In (1) the domain is from -infinity to +infinity. That is, you can input any value for x into the function, no problem. There is no value for x that is "forbidden". Likewise, the function "f" has no value that is out of it's range. So f has a range from -infinity to +infinity.
In (2), the domain is once again -infinity to +infinity. There is no value for x you cannot input. However, the range for the function g is different. It ranges from 1 to +infinity, this is because 1 is the lowest possible value you can get from the function... there is no real value for x you can input into g(x) so that it becomes less than 1.
In (3) the domain is any value between -infinity and +infinity,
except for -2/3. This is because if you input that value for x, you get division by zero, which is not allowed. The domain of h(x) is from -infinity to +infinity.
In (4) the domain is again -infinity and +infinity, but k(x) is limited... the maximum value of k(x) is 1, and the smallest is zero, so the range goes from 0 to 1.
So basically, when finding out the domain, you have to figure out what possible values for x you can plug into the function. Any value of x that leads to division by zero is a big no-no.
When finding out the range, you need to figure out what values the function can take. Like with the example of (4) for instance, there are no real values of x you can plug into the function to get any values for the function larger than 1, or smaller than 0...
There... that enough?
t:
nice one
