domain and range of graphs

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) for which the function is defined.

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 domain of a graph?

Back

To determine the domain of a graph, identify the x-values for which the graph exists. Look for any restrictions such as vertical asymptotes or holes.

Front

How do you determine the range of a graph?

Back

To determine the range of a graph, identify the y-values that the graph reaches. Look for any horizontal asymptotes or gaps in the y-values.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is all real numbers except x = 3.

Front

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

Back

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

Front

What does it mean if a function has a restricted domain?

Back

A restricted domain means that certain x-values are not included in the domain due to factors like division by zero or square roots of negative numbers.

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^2?

Back

The range is (-∞, 0] because the function produces non-positive values.

Front

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

Back

Interval notation uses brackets [ ] for inclusive endpoints and parentheses ( ) for exclusive endpoints.