Domain and Range of Functions

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

Is the relation {(1,2), (2,3), (1,4)} a function?

Back

No, because the input '1' has two different outputs (2 and 4).

Front

Identify the domain of f(x) = 1 / x.

Back

x ≠ 0.

Front

Identify the domain of f(x) = x.

Back

(-∞, ∞).

Front

Identify the domain of f(x) = 1 / (x - 5).

Back

x ≠ 5.

Front

What is the range of the function f(x) = x^2?

Back

[0, ∞) because the output is always non-negative.

Front

Identify the range of f(x) = 1 / x.

Back

(-∞, 0) ∪ (0, ∞).

Front

What does it mean for a relation to not be a function?

Back

It means that at least one input is associated with more than one output.

Front

Identify the domain of f(x) = √(x - 3).

Back

[3, ∞) because the expression under the square root must be non-negative.

Front

What is the range of a linear function?

Back

(-∞, ∞) because linear functions can take any real number as output.