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 based on its domain.

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 along the y-axis.

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 along the x-axis.

Front

What does it mean if the range of a function is expressed as [a, b]?

Back

It means that the range includes all values from a to b, including the endpoints a and b.

Front

What does it mean if the range of a function is expressed as (a, b)?

Back

It means that the range includes all values between a and b, but does not include the endpoints a and b.

Front

What does it mean if the domain of a function is expressed as [c, d]?

Back

It means that the domain includes all values from c to d, including the endpoints c and d.

Front

What does it mean if the domain of a function is expressed as (c, d)?

Back

It means that the domain includes all values between c and d, but does not include the endpoints c and d.

Front

What is the range of the function f(x) = x^2 for all real numbers x?

Back

The range is [0, ∞) because the output (y-values) is always non-negative.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, expressed as (-∞, 0) ∪ (0, ∞).