jacobe0008
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Drag and drop the answer into the box to identify each function as linear, exponential, or neither.


​x​ 2 3 4
f(x) 5.5 7 8.5
​x​ 0 3 6
f(x) 1 8 64

Respuesta :

​x​ 2 3 4
f(x) 5.5 7 8.5 

The first function is linear. When you subtract 5.5 from 7, you get 1.5 and when you subtract 7 from 8.5 you also get 1.5. That's how we know it's a linear function because there's clearly pattern. HOWEVER, if you had 5.5, 7, and 9 that would not be a linear function. Why? Because when you take away 7 from 9 you get 2. In order for it to be a linear function you have to get the same exact number when you subtract. 

x​ 0 3 6
f(x) 1 8 64 

The second function is exponential because when you divide you get the exact same number. 8/1 = 8 and 64/8 = 8. So this is exponential. But if you had 72 instead of 64 it would not be an exponential function because there has to be a pattern. 

I hope this makes sense. Btw I had this question on my test too and this is correct. 

Using function concepts, it is found that:

  • The first function is linear.
  • The second function is exponential.

  • If the absolute value of the change is always the same, it is linear.
  • If the rate is the same, it is exponential.

In the first function:

[tex]8.5 - 7 = 7 - 5.5[/tex]

Absolute value always the same, hence linear.

In the second function:

[tex]\frac{64}{8} = \frac{8}{1}[/tex]

Rate always the same, hence exponential.

A similar problem is given at https://brainly.com/question/24282972

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