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. The function for inverse variation is y = k/x, where k is the constant of the inverse variation.
b. To find the constant of the inverse variation, you can use two points from the relationship and solve for k.
c. In the inverse variation situation, y is the dependent variable and x is the independent variable.
d. The domain consists of all real numbers except x = 0 because division by zero is undefined. The range consists of all real numbers except y = 0.
e. The x-axis and y-axis are asymptotes for the graph of an inverse variation equation because the function will approach but never reach 0 on both axes.
f. To graph the function, plot points and draw a smooth curve that gets closer to the x-axis and y-axis but never crosses them, indicating the asymptotes.