Find the domain of the function $$f(x) = \frac{1}{x-5}$$ .

The domain is $$\{x \ne 5\}$$ .

Find the domain of the function $$f(x) = \frac{x}{x^2 - 16}$$ .

The domain is $$\{x \ne -4, 4\}$$ .

Find the domain of the function $$g(x) = \sqrt{2x - 4}$$ .

The domain is $$\{x \ge 2\}$$ .

What is the domain of a square root function?

The domain of a square root function is the set of all x-values for which the expression inside the square root is non-negative.

What is the domain of the function $$f(x) = \frac{1}{x^2 - 1}$$ ?

The domain is $$\{x \ne 1, -1\}$$ .

How do you find the domain of a function algebraically?

To find the domain, identify values that make the function undefined (like division by zero or negative square roots) and exclude them from the set of real numbers.

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

The domain is $$\{x \ge -1\}$$ .

What is the domain of the function $$f(x) = \frac{1}{x^2 + 4}$$ ?

The domain is all real numbers, or $$(-\infty, \infty)$$ , since the denominator is never zero.

What is the domain of the function $$f(x) = \sqrt{x^2 - 4}$$ ?

The domain is $$\{x \le -2\} \cup \{x \ge 2\}$$ .

What is the domain of the function $$f(x) = \frac{x + 2}{x - 3}$$ ?

The domain is $$\{x \ne 3\}$$ .

Domain Algebraically Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the definition of 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

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is the domain of a polynomial function?

Back

7.

FLASHCARD QUESTION

Front

What is the domain of a rational function?

Back

The domain of a rational function is all real numbers except where the denominator is zero.

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