Domain and Range rti

Front

What is the definition of 'Domain' in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of 'Range' in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

Front

How do you determine the domain of a function from its graph?

Back

The domain is found by identifying the x-values that the graph covers, reading from left to right.

Front

How do you determine the range of a function from its graph?

Back

The range is found by identifying the y-values that the graph covers, reading from bottom to top.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2, which can be expressed as (-∞, 2) ∪ (2, ∞).

Front

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

Back

The range is [0, ∞) because the output of x^2 is always non-negative.

Front

What does it mean if a function has a domain of (-3, 3]?

Back

It means that the function is defined for all x-values greater than -3 and up to and including 3.

Front

What does it mean if a function has a range of [-15, ∞)?

Back

It means that the function outputs values starting from -15 and going up to infinity, including -15.

Front

If a function's graph does not touch the x-axis, what can be said about its range?

Back

If the graph does not touch the x-axis, the range does not include zero.

Front

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

Back

The domain is [1, ∞) because the expression under the square root must be non-negative.