Graphing Exponential and Logarithmic Functions

This video tutorial covers graphing exponential and logarithmic functions, focusing on transformations such as vertical stretch, compression, and reflection. It uses caffeine decay as a practical example to illustrate exponential decay and how transformations affect graph shapes. The tutorial also explains how to apply these transformations to model real-world scenarios, like caffeine consumption, and provides strategies for accurately plotting graphs.

What is the y-intercept of an exponential function in the form y = b^x?

• 0

• 1

• b

• x

If caffeine decreases by 12% per hour, what is the base of the exponential decay function?

• 1.12

• 0.88

• 1.88

• 0.12

How does multiplying an exponential function by a constant greater than 1 affect its graph?

• It compresses the graph vertically.

• It shifts the graph horizontally.

• It stretches the graph vertically.

• It reflects the graph over the x-axis.

What happens to the graph of a function if it is multiplied by a negative constant?

• It shifts upwards.

• It compresses vertically.

• It reflects over the x-axis.

• It stretches horizontally.

What is the first step in graphing an exponential function?

• Draw the asymptote.

• Identify the parent function.

• Multiply by a constant.

• Plot random points.

Which transformation does not change the shape of the graph?

• Vertical compression

• Horizontal shift

• Vertical stretch

• Vertical reflection

What should you do to increase the accuracy of your graph?

• Use a calculator

• Use a ruler

• Draw freehand

• Plot a few points