Q1. Graph the exponential function by making a table of coordinates.

Background

Topic: Exponential Functions

This question is testing your ability to graph exponential functions by creating a table of values (t-table) and plotting the corresponding points on a coordinate grid.

Key Terms and Formulas

• Exponential Function: where and

• t-table: A table listing values of and their corresponding values

Step-by-Step Guidance

1. Choose 3–5 values for (for example: ).

2. Calculate for each chosen using the exponential formula .

3. Fill in the t-table with your values and corresponding values.

4. Plot each ordered pair on the provided coordinate grid.

Try solving on your own before revealing the answer!

Q2. Graph the logarithmic function and its inverse (exponential function) in the same coordinate system.

Background

Topic: Logarithmic Functions and Their Inverses

This question is testing your understanding of how logarithmic functions are the inverses of exponential functions, and how their graphs relate to each other.

Key Terms and Formulas

• Logarithmic Function: where and

• Inverse Relationship: and (or )

• Reflection: The graph of the logarithmic function is a reflection of the exponential function about the line .

Step-by-Step Guidance

1. Graph the exponential function by plotting points as in the previous question.

2. For the logarithmic function , switch the and values from the exponential function to get the points for the log function.

3. Plot both sets of points on the same coordinate grid.

4. Draw the line to visualize the reflection relationship.

Try solving on your own before revealing the answer!