Finding Appropriate Domain & Range SHORT

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 maximum or minimum values.

Front

What does it mean for a function to have 'all real numbers' as its domain?

Back

It means that the function is defined for every possible real number input without any restrictions.

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What does it mean for a function to have 'non-negative real numbers' as its domain?

Back

It means that the function is only defined for values of x that are greater than or equal to zero.

Front

What is the domain of a quadratic function that opens upwards?

Back

The domain of a quadratic function that opens upwards is all real numbers.

Front

What is the range of a quadratic function that opens upwards with a vertex at (h, k)?

Back

The range is all real numbers y such that y ≥ k, where k is the y-coordinate of the vertex.

Front

What is the significance of the vertex in determining the range of a quadratic function?

Back

The vertex represents the maximum or minimum point of the function, which helps define the lowest or highest value in the range.

Front

How can you identify restrictions on the domain from a graph?

Back

Restrictions can be identified by looking for vertical asymptotes, holes, or endpoints in the graph.