Domain and Range

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 function from its graph?

Back

The domain can be determined by identifying the x-values for which the graph exists, including any restrictions such as holes or vertical asymptotes.

Front

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

Back

The range can be determined by identifying the y-values that the graph reaches, including any restrictions such as horizontal asymptotes.

Front

What does it mean if the range of a function is expressed as y ≤ 2.5?

Back

It means that the output values (y) of the function can be any value less than or equal to 2.5.

Front

What does it mean if the domain of a function is expressed as 0 ≤ t ≤ 4.5?

Back

It means that the input values (t) of the function can be any value from 0 to 4.5, inclusive.

Front

What is the significance of open and closed intervals in domain and range?

Back

Open intervals (e.g., (a, b)) do not include the endpoints, while closed intervals (e.g., [a, b]) include the endpoints, affecting the values that can be taken.

Front

How can you express the range of a function that has a minimum value of -3 and approaches but never reaches 1?

Back

The range can be expressed as -3 ≤ y < 1.

Front

What is the domain of a function that is defined for all real numbers except x = -7 and x = 5?

Back

The domain can be expressed as (-∞, -7) ∪ (-7, 5) ∪ (5, ∞).

Front

How do you find the range of a quadratic function?

Back

For a quadratic function in the form y = ax^2 + bx + c, the range can be determined by finding the vertex and the direction of the parabola (upward or downward).