Inverse Variation/Radicals/Rational Flashcard

Front

What is inverse variation?

Back

Inverse variation describes a relationship between two variables in which the product of the variables is constant. If y varies inversely with x, then y = k/x, where k is a non-zero constant.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where a function approaches infinity or negative infinity as the input approaches a.

Front

How do you find the domain of a rational function?

Back

The domain of a rational function is found by identifying the values of x that make the denominator zero and excluding them from the set of all real numbers.

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 based on its domain.

Front

How do transformations affect the graph of a function?

Back

Transformations such as translations, reflections, and stretches/compressions change the position and shape of the graph of a function.

Front

What does it mean to reflect a graph over the x-axis?

Back

Reflecting a graph over the x-axis means that for every point (x, y) on the graph, the point (x, -y) will also be on the graph.

Front

What is the effect of translating a graph 4 units to the left?

Back

Translating a graph 4 units to the left involves replacing x with (x + 4) in the function's equation.

Front

What is the significance of the constant k in inverse variation?

Back

The constant k in inverse variation represents the product of the two variables and determines the strength of the relationship between them.

Front

How do you identify the constant k in an inverse variation equation?

Back

To identify the constant k, you can multiply the values of x and y from a point on the graph or from given values in the equation.

Front

What is the general form of a rational function?

Back

The general form of a rational function is f(x) = P(x)/Q(x), where P(x) and Q(x) are polynomials.