Does this table represent a function? Why or why not?
1 answer:
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Answer:
Step-by-step explanation:
From inspection of the graph, the given points are:
- (2, 9)
- (3, 3)
- (4, 1)
If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.
<u>General form</u> of a geometric sequence:
where:
- a is the first term
- r is the common ratio
is the nth term
Rewrite the given points as terms of the sequence:
- (2, 9) ⇒ a₂ = 9
- (3, 3) ⇒ a₃ = 3
- (4, 1) ⇒ a₄ = 1
To find the common ratio r, divide consecutive terms:
Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:
Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:
Learn more about geometric sequences here: