https://file.aiquickdraw.com/mathbot/file/1727380475507uyi444tl.jpg

You are asked to complete the table of values for \( y = 2^x \).

### Given table:
| \( x \)  | -2   | -1   | 0    | 1   | 2   | 3   |
|----------|------|------|------|-----|-----|-----|
| \( y \)  | 0.25 | ?    | ?    | ?   | 2   | ?   |

To complete this table, we need to calculate \( y = 2^x \) for each value of \( x \).

### Steps:
1. \( x = -2 \): \( y = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} = 0.25 \) (this value is already given)
2. \( x = -1 \): \( y = 2^{-1} = \frac{1}{2} = 0.5 \)
3. \( x = 0 \): \( y = 2^0 = 1 \)
4. \( x = 1 \): \( y = 2^1 = 2 \) (already given)
5. \( x = 2 \): \( y = 2^2 = 4 \)
6. \( x = 3 \): \( y = 2^3 = 8 \)

### Completed table:
| \( x \)  | -2   | -1   | 0    | 1   | 2   | 3   |
|----------|------|------|------|-----|-----|-----|
| \( y \)  | 0.25 | 0.5  | 1    | 2   | 4   | 8   |

Would you like more details or any clarifications on how the values were calculated?

### Related questions:
1. How do you compute negative exponents like \( 2^{-x} \)?
2. What is the pattern in the table of values for \( y = 2^x \)?
3. How does changing the base of the exponent affect the graph of the function?
4. What happens when the exponent is a fraction or a decimal?
5. Can you predict the behavior of \( y = 2^x \) as \( x \) approaches very large negative or positive values?

### Tip:
For exponential functions, values grow rapidly for positive exponents and approach zero for negative exponents.

Complete the table of values for y = 2^x.

Learn how to complete the table of values for the exponential function y = 2^x. This question covers the concepts of exponential growth and negative exponents, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation