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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.A.1

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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).