SOLUTION: State the domain of the following: h(x)= 3x^2+5x-3

Question 115347: State the domain of the following:
h(x)= 3x^2+5x-3
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
The domain of a function of x is the spectrum of values that x can take.
.
The given function is shown in the following graph:
.

.
Notice that there are no unusual happenings with this function. As x gets bigger and bigger
in the positive direction, the graph will just continue getting bigger and bigger in the
upward direction. And as x goes more and more in the negative direction, the graph will again
get bigger and bigger in the upward direction. For every value of x on the x-axis there
will be a single corresponding value on the graph of the function.
.
Therefore, you can say that the values that x will be allowed to take (that is the domain
of x) are all real numbers from minus infinity to positive infinity.
.
Hope this helps you to understand what is meant by the domain of x and how you can look
at it. If you are given a function of x that involves a square root of a term involving
x or a denominator that is a function of x, be careful. Remember that the square root can only
be taken for a positive quantity, and a denominator cannot be zero because division
by zero is not allowed. These are the types of things that can affect what values that
the domain of x cannot include. But this problem did not involve any limits such as these.
.
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