IXL - Identify linear and exponential functions (Algebra 2 practice)

A function

(

)

increases by 1 over every unit interval in

and

(

)

Which could be a function rule for

(

)

(

)

–

(

)

(

)

(

)

–

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Learn with an example

question

A function

(

)

increases by a factor of 10 over every unit interval in

and

(

)

Which could be a function rule for

(

)

(

)

(

)

–

(

)

(

)

–

solution

A unit interval in

is an interval of length 1. Its endpoints can be written as

and

where

is a real number.

Since

(

)

increases by a factor of 10 over every unit interval:

(

)

(

)

Find a function rule.

Start with

(

)

and write down a few values of the function and look for a pattern.

(

)

(

)

(

)

(

)

(

)

(

)

(

)

This suggests the function rule for

(

)

Confirm that your function rule is correct.

To confirm that

(

)

increases by a factor of 10 over every unit interval, compute the ratio of its values at the endpoints

and

(

)

(

)

Divide by subtracting the exponents

(

)

–

Divide by subtracting the exponents

Notice that

(

)

(

)

does not depend on

;

it always equals 10. This confirms that

(

)

increases by a factor of 10 over every unit interval in

So, the correct answer is:

(

)

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Work it out

Not feeling ready yet? These can help:

AA.8Linear functions over unit intervals

Z.6Exponential functions over unit intervals

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