a Think of pairs of numbers that when multiplied give 64.
B
b Plot the points in the coordinate plane.
C
c Recall the types of functions. Solving the equation from Part A for y can be useful.
A
a See solution.
B
b See solution.
C
c If we connect the points that results in the same geometric mean, it would form a rational function y= ax. See solution.
Practice makes perfect
a We are asked to find five ordered pairs ( x, y) such that sqrt(x y)=8. To do this, let's notice that sqrt(64)=8. Therefore, we are looking for pairs that when multiplied give 64.
x
y
sqrt(xy)
1
64
8
2
32
8
4
16
8
8
8
8
16
4
8
b In this part, we are asked to plot the ordered pairs in a scatter plot.
c Looking at the graph we made in Part B, we can see that graphed points appear to be a rational function. We can make sure by solving the equation from Part A for y.
As we can see, the equation represents a rational function. Therefore, we can assume that if we connect the points that results in the same geometric mean it would form a rational function y= ax.
