To solve the problem, we need to match each equation with its corresponding colored graph. The black graph represents $y = 2^x$, and the other graphs are transformations of this basic exponential function.

Analyzing each equation:

1. $y = 2^x + 1$:

   • This equation represents a vertical shift of $y = 2^x$ by 1 unit upward.

2. $y = 2^x - 1$:

   • This represents a vertical shift of $y = 2^x$ by 1 unit downward.

3. $y = 2^{x-1}$:

   • This is a horizontal shift of $y = 2^x$ by 1 unit to the right.

4. $y = 2^{x+1}$:

   • This is a horizontal shift of $y = 2^x$ by 1 unit to the left.

Matching the graphs:

• Black graph (K): This is the standard $y = 2^x$ without any transformations.
• Orange graph (O): This graph appears to be shifted vertically upward, which matches the equation $y = 2^x + 1$.
• Red graph (R): This graph is shifted to the left, matching $y = 2^{x+1}$.
• Green graph (G): This graph is shifted to the right, corresponding to $y = 2^{x-1}$.
• Blue graph (B): This graph is shifted downward, matching $y = 2^x - 1$.

Final matching:

• $y = 2^x + 1$ → Orange (O)
• $y = 2^{x+1}$ → Red (R)
• $y = 2^{x-1}$ → Green (G)
• $y = 2^x - 1$ → Blue (B)

Would you like more details or have any questions? Here are some related questions to consider:

1. How do you identify vertical and horizontal shifts in exponential functions?
2. What happens if you shift an exponential function to the right or left by 2 units instead of 1?
3. How does changing the base of the exponential function affect the graph?
4. Can you describe the effect of multiplying the function by a constant?
5. What is the impact of reflecting an exponential function over the x-axis?

Tip: Vertical shifts occur by adding/subtracting constants outside the function, while horizontal shifts result from adding/subtracting constants inside the function.