Drag and drop the answer into the box to identify each function as linear, exponential, or neither.x 2 3 4f(x) 5.5 7 8.5 x 0 3 6f(x) 1 8 64
Accepted Solution
A:
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.