Piecewise Functions and Domain and Range

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions or formulas for different parts of its domain.

Front

What does the domain of a function represent?

Back

The domain of a function represents all the possible input values (x-values) for which the function is defined.

Front

What does the range of a function represent?

Back

The range of a function represents all the possible output values (y-values) that the function can produce.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input value corresponds to exactly one output value.

Front

What is the domain of the function f(x) = 2x + 3?

Back

The domain is (-∞, ∞) because this linear function is defined for all real numbers.

Front

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

Back

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

Front

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

Back

The domain is (-∞, 0) ∪ (0, ∞) because the function is undefined at x = 0.

Front

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

Back

The range is (-∞, 0] because the output values are always less than or equal to zero.

Front

How do you find the range of a piecewise function?

Back

To find the range, evaluate each piece of the function over its domain and combine the results.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents the relationship between input values and output values of a function.