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What type of function is represented by the table of values below?

O A. exponential
B. linear
OC. cubic
D. quadratic
X
1
2
3
4
5
y
4
8
12
16
20

User Danzel
by
8.4k points

1 Answer

6 votes

Answer:

B. linear

Explanation:

You want to know the type of function represented by the table of values ...

  • x: 1, 2, 3, 4, 5
  • y: 4, 8, 12, 16, 20

Differences

When the differences in x-values are 1 (or some other constant), the differences in y-values will tell you the kind of function you have.

Here, the "first differences" are ...

  • 8 -4 = 4
  • 12 -8 = 4
  • 16 -12 = 4
  • 20 -16 = 4

They are constant with a value of 4.

The fact that first differences are constant means the function is a first-degree (linear) function.

The table represents a linear function.

__

Additional comment

The function is y = 4x. That is, y is proportional to x with a constant of proportionality of 4.

The level at which differences are constant is the degree of the polynomial function. The differences of first differences are called "second differences," and so on. A cubic function will have third differences constant.

If differences are not constant, but have a constant ratio, the function is exponential.

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User Saurav Kumar Singh
by
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