Domain and Range - Algebra 1 (Honors)

Front

What is the definition of Domain in Algebra?

Back

The domain of a function is the complete set of possible values of the independent variable (x) that will not cause any undefined behavior in the function.

Front

What is the definition of Range in Algebra?

Back

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

Front

What does it mean for a graph to be Discrete?

Back

A discrete graph consists of distinct, separate points, indicating that the values of the variable are not continuous.

Front

What does it mean for a graph to be Continuous?

Back

A continuous graph is one that is unbroken and can be drawn without lifting the pencil from the paper, indicating that the variable can take on any value within a given range.

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 y-axis that the graph reaches.

Front

What is the range of the function f(x) = x^2 for x in [-3, 3]?

Back

The range is [0, 9] because the minimum value is 0 (at x=0) and the maximum value is 9 (at x=3 or x=-3).

Front

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

Back

The domain is all real numbers except x = 2, since the function is undefined at that point.

Front

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

Back

Interval notation uses brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints, e.g., [a, b) means a ≤ x < b.

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.

Front

What is the range of the function f(x) = -x + 4?

Back

The range is (-∞, 4] because as x increases, f(x) decreases without bound.