Question

Megan owns a clothing boutique. The table below represents the profit made, in dollars, every year since 2010, where x represents the number of years since 2010. Years since 2010 0 1 2 3 4 5

Profit (dollars) 39,000 84,000 111,000 120,000 111,000 84,000
Which of the following statements is true for this situation?

A.  Since the profit made in 2012 is equal to the profit made in 2014, the profit is          symmetric about the line  y  = 120,000.


B. The profit is not symmetric.
C.  Since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line  x  = 3.
D.  Since the profit made in 2011 is equal to the profit made in 2015, the profit is symmetric about the line  x  = 4.
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Answer 1

Answer:C. Since the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line x = 3.

Explanation:

Let the profit made by the boutique is given by the function y(x) then

We can see

Profit made in year 2011=profit made in year 2015

i.e.y(1)=y(5)=$84,000

profit made in year 2012=profit made in year 2014

i.e.y(2)=y(4)=$111,000

And profit made in year 2013 is standing in middle as y(3)=$120,000

which gives the line of symmetry x=3.(with reference to the figure)

Therefore, the profit made in 2012 is equal to the profit made in 2014, the profit is symmetric about the line x = 3.

Line of symmetry is an imaginary line that divides a line or shape making two identical halves.