How to find domain and range of a function without graph

College algebra students learn How to find domain and range of a function without graph, and manipulate different types of functions.

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Domain and Range

To find the domain, we must remember that: The denominator of a fraction cannot be equal to zero. The number under a square root cannot be a negative number. We determine the domain
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How to find domain and range of a function without graphing

For the constant function f(x)=c f ( x) = c, the domain consists of all real numbers; there are no restrictions on the input. The only output value is the constant c c, so the range is the set {c} { c

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Domain, Range and Codomain

1. Write the function as. f ( x) = 3 x 2 − 3 + 3 x 2 − 1 = 3 + 3 x 2 − 1. As f is even, we may suppose x ≥ 0, x ≠ q 1. Now the range of x 2 − 1 is [ − 1, + ∞) and for f ( x), the value x 2 = 1 is excluded

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From Graph

To find the domain of this type of function, just set the terms inside the radical sign to >0 and solve to find the values that would work for x. A function using the natural log (ln).