Graph the given function by making a table of coordinates.

f left parenthesis x right parenthesis equals 2 Superscript x
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Part 1
Complete the table of coordinates.
x
minus2
minus1
0
1
2
y
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
  
enter your response here
​(Type integers or fractions. Simplify your​ answers.)

1 answer

To complete the table of coordinates for the function \( f(x) = 2^x \), we will calculate \( f(x) \) for the given \( x \) values: -2, -1, 0, 1, and 2.

Let's calculate the values of \( y \):

  1. When \( x = -2 \): \[ f(-2) = 2^{-2} = \frac{1}{2^2} = \frac{1}{4} \]

  2. When \( x = -1 \): \[ f(-1) = 2^{-1} = \frac{1}{2^1} = \frac{1}{2} \]

  3. When \( x = 0 \): \[ f(0) = 2^0 = 1 \]

  4. When \( x = 1 \): \[ f(1) = 2^1 = 2 \]

  5. When \( x = 2 \): \[ f(2) = 2^2 = 4 \]

Now, we can fill in the table with the calculated values of \( y \):

| \( x \) | \( y = f(x) \) | |-----------|------------------| | -2 | \( \frac{1}{4} \) | | -1 | \( \frac{1}{2} \) | | 0 | 1 | | 1 | 2 | | 2 | 4 |

Complete Table of Coordinates:

  • \( (-2, \frac{1}{4}) \)
  • \( (-1, \frac{1}{2}) \)
  • \( (0, 1) \)
  • \( (1, 2) \)
  • \( (2, 4) \)

You can now use these coordinates to graph the function \( f(x) = 2^x \).