Q1. Draw the graph of the following function.

Background

Topic: Graphing Exponential Functions

This question tests your understanding of how to graph exponential functions and recognize their key features, such as intercepts, growth/decay behavior, and specific points on the graph.

Key Terms and Formulas

• Exponential Function: A function of the form , where and .

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

• Key Points: The y-intercept is always at for . Other points can be found by substituting values for .

Step-by-Step Guidance

1. Identify the base of the exponential function you are graphing. For example, if the function is , then .

2. Calculate and plot several key points, such as , , , and . For :

3. Draw the curve through these points, noting that the graph increases rapidly for positive (exponential growth) and approaches the x-axis (but never touches it) for negative $x$.

4. Label the y-intercept and other calculated points on your graph for clarity.

Try solving on your own before revealing the answer!