a.write a function that models an inverse variation situation
b.find the constant of the inverse variation
c.determine the dependent and independent variables
d.identify the domain and range
e.find the values of any asymptotes
f.graph the function, making sure to indicate any asymptotes
a. An inverse variation situation can be modeled by the equation y = k/x, where y is the dependent variable, x is the independent variable, and k is the constant of variation.
b. To find the constant of the inverse variation, you can use a given pair of x and y values and solve for k. For example, if x = 2 and y = 6, then k can be found by: 6 = k/2 -> k = 12. So the constant of the inverse variation is 12.
c. In the equation y = k/x, y is the dependent variable and x is the independent variable.
d. The domain of the function is all real numbers except for x = 0, as division by zero is undefined. The range of the function is all real numbers except for y = 0.
e. The function y = k/x has a vertical asymptote at x = 0 and a horizontal asymptote at y = 0.
f. To graph the function y = 12/x, plot the vertical asymptote at x = 0 and the horizontal asymptote at y = 0. Then, plot points such as (1, 12), (2, 6), and (3, 4) and draw a curve that approaches the asymptotes but does not cross them.