Find the domain of $$f(x) = \frac{1}{x-3}$$ .

The domain is all real numbers except x = 3, so the domain is $$(-\text{∞}, 3) igcup (3, \text{∞})$$ .

What is the domain of $$g(x) = \frac{\text{sqrt}{x-2}}{x-5}$$ ?

The domain is $$[2, 5) igcup (5, \text{∞})$$ .

Find the domain of $$f(x) = \text{sqrt}{7 - x}$$ .

The domain is $$(-\text{∞}, 7]$$ .

What is the domain of $$h(x) = \text{sqrt}{3x - 21} + 4$$ ?

The domain is $$[7, \text{∞})$$ .

Find the domain of $$f(x) = \text{sqrt[3]}{x + 2}$$ .

The domain is all real numbers, so the domain is $$(-\text{∞}, \text{∞})$$ .

What is the significance of the domain in a function?

The domain determines the valid input values for the function, which affects the function's graph and behavior.

How do you express the domain using interval notation?

Interval notation uses parentheses and brackets to denote open and closed intervals. For example, $$(a, b)$$ means a

What is an example of a function with a restricted domain?

The function $$f(x) = \text{sqrt}{x}$$ has a restricted domain of $$[0, \text{∞})$$ because the square root of a negative number is not defined in the real number system.

How do vertical asymptotes relate to the domain of a function?

Vertical asymptotes occur at values of x that are not in the domain of the function, typically where the denominator of a rational function equals zero.

What is the domain of $$f(x) = \text{log}(x-1)$$ ?

The domain is $$(1, \text{∞})$$ because the argument of the logarithm must be greater than zero.

How do you find the domain of composite functions?

To find the domain of composite functions, consider the domain of the inner function and ensure that the output of the inner function is within the domain of the outer function.

What is the domain of $$f(x) = \frac{1}{\text{sqrt}{x}}$$ ?

The domain is $$(0, \text{∞})$$ because x must be greater than zero to avoid division by zero and to keep the square root defined.

Algebraically Determining Domain of Functions Flashcard

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

2.

FLASHCARD QUESTION

Front

How do you determine the domain of a square root function?

Back

For a square root function, the expression inside the square root must be greater than or equal to zero. Set the inside expression ≥ 0 and solve for x.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

How do you find the domain of a rational function?

Back

For a rational function, set the denominator not equal to zero and solve for x. The domain is all real numbers except the values that make the denominator zero.

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

Back

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