Graph the given function by making a table of coordinates.

Question

f left parenthesis x right parenthesis equals 4 Superscript x
Question content area bottom
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.)

Answer 1

To graph the function \( f(x) = 4^x \), we can calculate the corresponding \( y \) values for the given \( x \) values in the table:

1. For \( x = -2 \): \[ f(-2) = 4^{-2} = \frac{1}{4^2} = \frac{1}{16} \]

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

3. For \( x = 0 \): \[ f(0) = 4^0 = 1 \]

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

5. For \( x = 2 \): \[ f(2) = 4^2 = 16 \]

Now, let's compile the \( x \) and \( y \) values into the table:

\[ \begin{array}{|c|c|} \hline x & y = f(x) \ \hline -2 & \frac{1}{16} \ -1 & \frac{1}{4} \ 0 & 1 \ 1 & 4 \ 2 & 16 \ \hline \end{array} \]

Summary Table of Coordinates:

• For \( x = -2 \), \( y = \frac{1}{16} \)
• For \( x = -1 \), \( y = \frac{1}{4} \)
• For \( x = 0 \), \( y = 1 \)
• For \( x = 1 \), \( y = 4 \)
• For \( x = 2 \), \( y = 16 \)

You can now use these coordinates to graph the function \( f(x) = 4^x \).