Domain and Range of Graphs

Front

What is the definition of 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.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the lowest and highest points on the graph and note the corresponding y-values.

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) that the function can accept.

Front

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the leftmost and rightmost points on the graph and note the corresponding x-values.

Front

What does it mean if the domain is 'all real numbers'?

Back

If the domain is 'all real numbers', it means that the function can accept any real number as an input.

Front

What does it mean if the range is '1 ≤ y ≤ 4'?

Back

It means that the output values of the function (y-values) can be any number from 1 to 4, inclusive.

Front

What is the significance of parentheses and brackets in interval notation?

Back

Parentheses indicate that the endpoint is not included in the interval, while brackets indicate that the endpoint is included.

Front

What is the domain of the function f(x) = √(x + 5)?

Back

The domain is x ≥ -5, since the expression under the square root must be non-negative.

Front

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

Back

The range is y ≥ 0, since the output of a square function is always non-negative.

Front

How can you express the domain of a function that is defined for all x except x = 3?

Back

The domain can be expressed as (-∞, 3) ∪ (3, ∞).