Hi!
I am stuck on the following question:-
What is the Domain and Range of f
I really have no clue and would be extremely grateful if someone could explain the procedure to this.
Many many thanks.
Swerve
this is a polynomial. the domain is all real x on the interval we are considering, since there is no restriction on what number we can choose. thus the domain (the set of input, in this case, x-values, we can choose) is $\displaystyle x \in [-3,3]$
the range is the set of y-values (output values) we have. this is an upward opening parabola, the minimum value occurs at the vertex, so $\displaystyle f(x) \ge -2$ for all $\displaystyle x$. we can see how high it goes by plugging in the end points. so the max value is $\displaystyle f(-3) = f(3) = 7$, thus, $\displaystyle \mbox{ran}f = [-2,7]$
graph the function to see what i'm talking about
you should ask new questions in a new thread.
open a new thread with these questions and show your working (whatever you are able to do) based on the following:
the domain of a function is the set of input values (usually x-values) for which the function is defined or works. for the above question, the function was defined for $\displaystyle -3 \le x \le 3$, so that was the domain. if that wasn't specified, then all real x would be the domain, that is, all $\displaystyle x \in \mathbb{R}$, since the unrestricted domain of polynomials is all real numbers, because any real number you plug in will work.
it is often easier to find what doesn't work and say the domain is everything but that. for example, for rational functions (functions that appear as fractions), the domain is all real numbers for which the denominator is NOT zero, provided there are no other restrictions; for example, the function contains squareroots (whose domain is all real numbers so that what is being squarerooted is greater than or equal to zero) or logs (whose domain is all real number so that what is being logged is greater than zero), etc.
the range is the set of output values (usually y-values) for which the function is defined, that is, all possible values we can obtain by plugging in any value from the domain
hope that helps.
The domain of a standard polynomial that doesn't have negative exponents is always infinite, for each and every real. The range for an even polynomial of this form is cut off in one direction, but unlimited in another. The range for an odd polynomial of this form is always infinite, spanning all real numbers.