domain and range of graphs

Front

What is the definition of domain in 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

How do you determine the domain of a graph?

Back

To determine the domain of a graph, identify the x-values that the graph covers, including any restrictions such as asymptotes or holes.

Front

What is the definition of range in 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 of a graph?

Back

To determine the range of a graph, identify the y-values that the graph covers, including any restrictions such as asymptotes or holes.

Front

What does the notation -3 < x ≤ 3 represent?

Back

This notation indicates that x can take any value greater than -3 and up to and including 3.

Front

What does the notation -4 ≤ x ≤ 3 represent?

Back

This notation indicates that x can take any value from -4 to 3, including both endpoints.

Front

What does the notation -2 < y < 2 represent?

Back

This notation indicates that y can take any value greater than -2 and less than 2.

Front

What is an example of a function with a restricted domain?

Back

An example is the square root function, f(x) = √x, which has a domain of x ≥ 0.

Front

What is an example of a function with a restricted range?

Back

An example is the sine function, f(x) = sin(x), which has a range of -1 ≤ y ≤ 1.

Front

What is the significance of vertical asymptotes in determining the domain?

Back

Vertical asymptotes indicate values of x where the function is undefined, thus restricting the domain.