Q13. Match the functions with one of the graphs A - F by writing the graph name on the line in front of the corresponding function from the list.

Background

Topic: Exponential Functions and Their Graphs

This question tests your ability to recognize and match exponential functions of the form to their corresponding graphs. You need to understand how the base and the coefficient affect the shape and direction of the graph.

Key Terms and Formulas:

• Exponential Function:

• Growth vs. Decay: If , the function shows exponential growth; if , it shows exponential decay.

• Vertical Stretch/Compression: The coefficient affects how steep or flat the graph is.

• Graph Direction: Growth functions rise as increases; decay functions fall as increases.

Step-by-Step Guidance

1. Review the list of functions: , , , , , .

2. Identify whether each function represents exponential growth or decay by examining the base :

   • If , it's growth.

   • If , it's decay.

3. Compare the coefficient (either 2 or 4) to determine which graphs are steeper (larger means steeper).

4. Look at the provided graph image and note the direction and steepness of each curve labeled A–F.

5. Match each function to the graph by considering both the base and the coefficient. For example, a function with and will be a steep decay curve.

6. Write the graph letter (A–F) next to each function based on your analysis, but do not reveal the final matches yet.

Try solving on your own before revealing the answer!