5.3: Range of a Function

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 based on its domain.

Front

What does the notation [-2, 5] represent?

Back

It represents a closed interval including all numbers from -2 to 5, where -2 and 5 are included in the range.

Front

What does the notation (1, ∞) represent?

Back

It represents an open interval starting just above 1 and extending to infinity, meaning 1 is not included in the range.

Front

How do you determine the range from a set of ordered pairs?

Back

The range is found by identifying all the second elements (y-values) from the ordered pairs.

Front

What is the range of the function represented by the points (2, 4), (5, 5), (8, 6), (11, 7)?

Back

The range is {4, 5, 6, 7}.

Front

What is the difference between a closed interval and an open interval?

Back

A closed interval includes its endpoints, while an open interval does not.

Front

If a function has a range of y ≤ 1, what does this imply about its outputs?

Back

It implies that all output values (y-values) are less than or equal to 1.

Front

What is the range of the function f(x) = x^2 for x ≥ 0?

Back

The range is [0, ∞) because the smallest value of x^2 is 0 when x = 0.

Front

What is the range of the function f(x) = -x for all real numbers x?

Back

The range is all real numbers, (-∞, ∞), because the function can produce any y-value.

Front

How can you express the range of a function using set notation?

Back

The range can be expressed using curly braces, e.g., {y | y is an output of the function}.