Algebra 2: Transformations of Exponential and Logarithmic Functions

This video tutorial covers section 6.4 of Algebra 2, focusing on transformations of exponential and logarithmic functions. It explains how to apply transformations such as stretching, flipping, and shifting to these functions, and discusses the impact on their graphs and asymptotes. The tutorial includes examples and exercises to reinforce understanding, and concludes with assignment instructions.

What is the main focus of section 6.4 in Algebra 2?

• Graphing linear equations

• Transformations of exponential and logarithmic functions

• Understanding polynomial functions

• Solving quadratic equations

Which variable represents the base of an exponential function in transformations?

• D

• B

• A

• C

What effect does a negative multiplier on X have on a graph?

• Shift down

• Shift up

• Horizontal flip

• Vertical stretch

In the example of G(x) = (1/3)^(x+2) - 2/3, what transformation occurs due to the '+2' in the exponent?

• Shift down 2 units

• Shift left 2 units

• Shift right 2 units

• Shift up 2 units

What transformation is caused by a negative sign in front of the input of a logarithmic function?

• Shift down

• Shift up

• Horizontal flip

• Vertical flip

How does subtracting a number from the input of an exponential function affect its graph?

• Shifts the graph up

• Shifts the graph right

• Shifts the graph down

• Shifts the graph left

What is the new vertical asymptote for a logarithmic function shifted one unit to the right?

• x = 1

• y = 0

• y = 1

• x = 0

When constructing a new function by shifting e^(-x) four units to the right, what is the new input?

• x + 4

• -x + 4

• x - 4

• -x - 4

What does a horizontal stretch imply about the speed of a function's graph?

• It remains the same

• It moves slower

• It moves faster

• It flips vertically

In the transformation of a natural log function, what does adding a number outside the logarithm do?

• Shifts the graph left

• Shifts the graph right

• Shifts the graph up

• Shifts the graph down