6. Analyzing Functions with Successive Differences
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Calculate the differences and ratios between consecutive terms. Are either of these the same throughout the sequence?
Type of Function: Exponential
Function: y=3×3x
We want to tell whether the table of values represents a linear, exponential, or quadratic function. To do so, we will analyze how the consecutive terms are related to each other.
x | -1 | 0 | 1 | 2 | 3 |
---|---|---|---|---|---|
y | 1 | 3 | 9 | 27 | 81 |
Let's begin with calculating the first differences.
The first differences are not all equal. Therefore, the table of values does not represent a linear function. Let's find the second differences and compare them.
x=0, y=3
a0=1
Identity Property of Multiplication
Rearrange equation