Myra uses an inverse variation function to model the data for the ordered pairs. open paren 2 comma 30 close paren , open paren 3 comma 20 close paren , open paren 4 comma 15 close paren , open paren 5 comma 12 close paren , open paren 6 comma 10 close paren Which statement best explains whether an inverse variation function is the best model for the data?
Answer
A
An inverse variation function is not the best model because data points approximate a straight line.
B
An inverse function is the best model because the products of corresponding x - and y -values are equal.
C
An inverse function is the best model because as x increases, y decreases.
D
An inverse variation function is not the best model because the data points show an exponential decay.
Explanation
For an inverse variation, the product of each corresponding x- and y-value must be constant. Here, 2 × 30 = 60, 3 × 20 = 60, 4 × 15 = 60, 5 × 12 = 60, and 6 × 10 = 60. Since all the products are equal, an inverse variation is a good model for the data; this matches the choice stating that the products are equal.
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