Inverse Variation/Radicals/Rational Flashcard

Front

What is inverse variation?

Back

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

Front

How do you find the constant of variation (k) in inverse variation problems?

Back

To find the constant of variation (k), multiply the values of x and y when they are known. For example, if y = 10 when x = 5, then k = 10 * 5 = 50.

Front

What is the formula for inverse variation?

Back

The formula for inverse variation is y = k/x, where k is the constant of variation.

Front

What does it mean for a function to have a vertical asymptote?

Back

A vertical asymptote is a line x = a where the function approaches infinity or negative infinity as x approaches a. It indicates that the function is undefined at that point.

Front

How do you determine the vertical asymptote of a rational function?

Back

To find the vertical asymptote of a rational function, set the denominator equal to zero and solve for x.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a line y = b that the graph of a function approaches as x approaches infinity or negative infinity.

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote of a rational function, compare the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, y = 0 is the horizontal asymptote.

Front

What is the effect of translating a function on its graph?

Back

Translating a function shifts its graph horizontally and/or vertically without changing its shape.

Front

How do you translate the function y = 1/x to the left by 2 units and down by 4 units?

Back

To translate y = 1/x to the left by 2 units, replace x with (x + 2). To translate down by 4 units, subtract 4 from the entire function, resulting in y = 1/(x + 2) - 4.

Front

What is the significance of the intersection of asymptotes in a rational function?

Back

The intersection of asymptotes indicates the point where the vertical and horizontal asymptotes meet, which can provide insight into the behavior of the function near that point.