**Determine the Type of Function; Explain Your Reasoning****Given Data:**| Input | Output ||-------|--------|| -4 | 0.125 || -3 | 0.25 || -2 | 0.5 || -1 | 1 || 0 | 2 || 1 | 4 || 2 | 8 || 3 | 16 || 4 | 32 |**Analysis and Explanation:**To determine the type of function represented by the given data, we'll first observe the relationship between the input and output values. Notice that as the input values increase or decrease by 1, the output values are either multiplied or divided by 2 correspondingly.For example:- When the input goes from -1 to 0, the output changes from 1 to 2 (i.e., \(1 \times 2 = 2\)).- When the input goes from 0 to 1, the output changes from 2 to 4 (i.e., \(2 \times 2 = 4\)).This suggests that the relationship between input (x) and output (y) can be expressed as:\[ y = 2^{x+1} \]By verifying this, for each input value, we can confirm that the output value adheres to this function:- For \( x = -4 \), \( y = 2^{-3} = 0.125 \)- For \( x = -3 \), \( y = 2^{-2} = 0.25 \)- For \( x = -2 \), \( y = 2^{-1} = 0.5 \)- For \( x = -1 \), \( y = 2^{0} = 1 \)- For \( x = 0 \), \( y = 2^{1} = 2 \)- For \( x = 1 \), \( y = 2^{2} = 4 \)- For \( x = 2 \), \( y = 2^{3} = 8 \)- For \( x = 3 \), \( y = 2^{4} = 16 \)- For \( x = 4 \), \( y = 2^{5}

Name: **Determine the Type of Function; Explain Your Reasoning****Given Dat
Uploaded: 2024-03-20T06:47:22.000Z
Channel: Bartleby
Description: **Determine the Type of Function; Explain Your Reasoning****Given Data:**| Input | Output ||-------|--------|| -4 | 0.125 || -3 | 0.25 || -2 | 0.5 || -1 | 1 || 0 | 2 || 1 | 4 || 2 | 8 || 3 | 16