Domain Algebraically

Front

What is the definition of a rational function?

Back

A rational function is a function that can be expressed as the ratio of two polynomials, i.e., \( f(x) = \frac{P(x)}{Q(x)} \) where \( P(x) \) and \( Q(x) \) are polynomials and \( Q(x) \neq 0 \).

Front

How do you find the domain of a rational function?

Back

To find the domain of a rational function, identify the values of \( x \) that make the denominator zero and exclude them from the domain.

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

How do you find the domain of a square root function?

Back

To find the domain of a square root function, set the expression inside the square root greater than or equal to zero and solve for \( x \).

Front

What is 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 range of a quadratic function?

Back

The range of a quadratic function \( f(x) = ax^2 + bx + c \) can be determined by finding the vertex and identifying whether it opens upwards or downwards.

Front

What is the process of factoring a quadratic expression?

Back

To factor a quadratic expression \( ax^2 + bx + c \), find two numbers that multiply to \( ac \) and add to \( b \), then rewrite the expression using these numbers.

Front

Factor completely: 2x² + x - 6

Back

(x + 2)(2x - 3)

Front

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

Back

The vertex of a quadratic function represents the maximum or minimum point of the graph, depending on whether it opens upwards or downwards.

Front

What is the difference between open and closed intervals?

Back

An open interval (a, b) does not include the endpoints a and b, while a closed interval [a, b] includes both endpoints.