What is the domain of $$f(x) = \frac{1}{x-5}$$ ?

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

What is the domain of $$f(x) = \frac{x}{x^2-16}$$ ?

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

What is a linear function?

A linear function is a function that graphs to a straight line and can be expressed in the form $$f(x) = mx + b$$ where m is the slope and b is the y-intercept.

What is the domain of a linear function?

The domain of a linear function is all real numbers, expressed as $$\{-\infty

What is a radical function?

A radical function is a function that contains a variable within a radical (square root, cube root, etc.), typically in the form $$f(x) = \sqrt{x}$$ .

How do you find the domain of a radical function?

To find the domain of a radical function, set the expression inside the radical greater than or equal to zero and solve for x.

What is the difference between a function and a non-function?

A function assigns exactly one output for each input, while a non-function may assign multiple outputs for a single input.

What is a logarithmic function?

A logarithmic function is the inverse of an exponential function and is typically expressed as $$f(x) = \log_b(x)$$ where b is the base.

What is the domain of a logarithmic function?

The domain of a logarithmic function is all positive real numbers, expressed as $$\{x > 0\}$$ .

What is the significance of identifying the domain of a function?

Identifying the domain of a function is crucial because it determines the valid input values for which the function produces real outputs.

Domain from Functions Flashcards

Student preview

15 questions

Show all answers

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 a rational function?

Back

3.

FLASHCARD QUESTION

Front

How do you find the domain of a rational function?

Back

To find the domain of a rational function, identify the values of x that make the denominator zero and exclude them from the domain.

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What is an absolute value function?

Back

7.

FLASHCARD QUESTION

Front

What is the domain of an absolute value function?

Back

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