IXL - Identify linear, quadratic, and exponential functions from tables (Algebra 1 practice)

Is this function linear, quadratic, or exponential?

x	y
– 1	2
0	4
1	8
2	16
3	32

linear

quadratic

exponential

ref_doc_title.

Learn with an example

question

Is this function linear, quadratic, or exponential?

x	y
– 9	– 162
– 8	– 128
– 7	– 98
– 6	– 72
– 5	– 50

linear

quadratic

exponential

key idea

You can determine if a function is linear, quadratic, or exponential by looking at the pattern of

-values.

solution

Since the

-values

in the table are consecutive, you can compare successive

-values

to determine which type of function the table describes.

You can test whether a function is linear by finding the differences between successive

-values,

which are called the first

differences.

If the first differences are all equal, the function is linear.

Find the first differences in the table.

x	y
– 9	– 162	+ 34
– 8	– 128	+ 30
– 7	– 98	+ 26
– 6	– 72	+ 22
– 5	– 50

Since the first differences are not all equal, the function can't be linear.

You can test whether a function is quadratic by finding the differences between successive first differences, which are called the second

differences.

If the second differences are all equal, the function is quadratic.

Find the second differences in the table.

x	y
– 9	– 162	+ 34
– 8	– 128	+ 30	– 4
– 7	– 98	+ 26	– 4
– 6	– 72	+ 22	– 4
– 5	– 50

Since the second differences are all

–

the function is quadratic.

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Teacher tools

Work it out

Not feeling ready yet? These can help:

AA.3Identify linear and exponential functions from tables

FF.4Sequences: mixed review

AA.2Identify linear, quadratic, and exponential functions from graphs

D.8Add, subtract, multiply, or divide two decimals

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