**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
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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

We need to find the type of function represented by the given set of values in the table. Fact Used:…

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Math

Trigonometry

Determine the type of function; explain your reasoning. Input Output -4 0.125 -3 0.25 -2 0.5 -1 1 0. 2. 1 4 8. 2.

Trigonometry (11th Edition)

11th Edition

ISBN:9780134217437

Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels

Chapter1: Trigonometric Functions

Section: Chapter Questions

Problem 1RE: 1. Give the measures of the complement and the supplement of an angle measuring 35°.

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Topic Video

Question

**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}

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