Which equation describes the relationship between the variables in the table below?
2 answers:
Answer:
Option D
Step-by-step explanation:
x y_
-1 0.1
1 9
2 81
4 6,561
5 59,049
We are given the above table for x and y
We are asked to find the graph
Consider
When x=-1, y =1/9 = 0.1
x=1 y =9, when x=2,y = 81 and so on
x=5, y = 9^5 =59049
Hence the correct equation is
because each y value is the previous y value multiplied by 9
Option D is right
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Since x can't be zero (it sits at the denominator of the left hand side), let's split cases:
If x is positive
It this case, we can multiply both sides by x without changing the inequality sign:
But since we're assuming that x is positive, we can only accept the numbers between 0 and 1.
If x is negative
It this case, in order to multiply both sides by x we have to change the inequality sign:
But since we're assuming that x is negative, we can only accept the numbers which are smaller than -1.
So, putting all the pieces together, we have that the solution is given by the following interval: