Px = x² -2x +15
Am I to substitute numbers for x?
Please show me how it is done
Since no domain is specified, we take the natural domain, which is the set of values for which the function is defined. Assuming we are working in the reals, the domain here is simply $\displaystyle \mathbb{R}$.
If you had something like $\displaystyle \displaystyle f(x)=\frac{1}{1-x}$ then the domain would be $\displaystyle \mathbb{R} \setminus \{1\}$.
$\displaystyle P(x) = x^2 - 2x + 15$
Are you being asked for the set of values that make up the domain?
If so, ask yourself if there are any values of x that you cannot use. For instance, if you look at another function
$\displaystyle f(x) = \frac{1}{x-1}$,
you would see that the domain of f(x) is all real numbers except x = 1, because you can't have a 0 in the denominator. Now, look at this function:
$\displaystyle f(x) = \sqrt{x+5}$.
The domain of g(x) is $\displaystyle x \geq -5$, because if you let x equal a number less than -5 you would get a negative number in the square root, which is invalid.
The above are two instances where the domain of a function could be restricted. A third would be if the function represent a model. For instance, if you are modeling an area of a rectangular field, the lengths of the sides must be positive.
So, I'll ask again: are there any values of x that you cannot use?
EDIT: Ack, beaten to it!
Hello eumyang,
I get what you are explaining to me. The value can be used except for that which will make the equation =0
I cannot answer your question in reference to "Are there any values of x that you cannot use?
The question would be what is the domain of P? Could it simply be all real numbers?
X/X is a real set of numbers
or is it
X/X is a real number and X (not equal) to 5
X/X is a real number and X (not equal) to 0
X/X is a real number and X >0
Once again, the domain of a function is the set of values that $\displaystyle x$ can take.
If you don't understand the "algebraic", it sounds like you need more grounding with the "graphical" and the "numerical".
Graph the function of $\displaystyle P(x) = x^2 - 2x + 15$
Now think if you were to start at one end of the graph and follow it, would you ever have to stop?
Actually, that's not what I said. Values of x that make the denominator of a fraction 0, or an expression underneath a square root negative, would not be part of the domain.
What I was getting at was this: does the function P have a fraction or a square root? If no for both, then likely the domain is all reals. In fact, all quadratics in the formI cannot answer your question in reference to "Are there any values of x that you cannot use?
The question would be what is the domain of P? Could it simply be all real numbers?
$\displaystyle f(x) = Ax^2 + Bx + C$
(where A, B and C are real number coefficients and A is not zero)
... have a domain of all real numbers.