Question

the graph of f(x)-2^x is shown in black(K).
Match each transformation of this function with a graph below.
2^-x
-2^x
-2^-x
a. red (R)
b. blue (B)
c. green (G)

Answer 1

To match the transformations of the function \( f(x) = 2^x \) with their corresponding graphs, let's first analyze each transformation:

1. **\( f(x) = 2^{-x} \)**:
- This reflects the graph of \( f(x) = 2^x \) across the y-axis.
- Therefore, the graph would look similar to the original but mirrored horizontally.

2. **\( f(x) = -2^x \)**:
- This reflects the original graph across the x-axis.
- The graph will be inverted, appearing below the x-axis.

3. **\( f(x) = -2^{-x} \)**:
- This is the same as first reflecting \( f(x) = 2^x \) across the y-axis (to get \( 2^{-x} \)) and then reflecting that result across the x-axis.
- This will make the graph inverted and mirrored, so it appears below the x-axis and also reflected.

Now, if you have the graphs labeled as red (R), blue (B), and green (G), the assignment would typically be as follows:

- **Red (R)**: Corresponds to \( 2^{-x} \)
- **Blue (B)**: Corresponds to \( -2^x \)
- **Green (G)**: Corresponds to \( -2^{-x} \)

Please verify this information using the actual graphs for confirmation.