Understanding Logarithmic Transformations

The video tutorial covers logarithmic functions, focusing on graphing them and understanding their transformations. It begins with an introduction to logarithmic functions and their parent graphs. The tutorial then explains how to graph logarithms and compares them to their parent graphs. The main focus is on transformations, including shifts and reflections, and how these affect the graph. The tutorial concludes with practical examples of applying transformations to logarithmic graphs.

What is the general form of a logarithmic function?

• y = x^2

• y = sin(x)

• y = log(x)

• y = e^x

Where is the y-intercept of the parent logarithmic graph?

• (0, 0)

• (0, 1)

• (1, 0)

• (1, 1)

What is the significance of the point (1, 0) in the parent graph?

• It is the vertex

• It is the y-intercept

• It is the x-intercept

• It is the asymptote

What does the 'a' in the transformation equation y = a * log(x) indicate?

• Vertical shift

• Horizontal shift

• Reflection over the x-axis

• Change in base

What is the effect of a negative 'a' in the transformation equation?

• Shifts the graph left

• Reflects the graph over the x-axis

• Shifts the graph right

• Reflects the graph over the y-axis

How does the 'H' in the transformation equation affect the graph?

• Changes the slope of the graph

• Shifts the graph left or right

• Reflects the graph over the y-axis

• Shifts the graph up or down

What is the effect of a positive 'K' in the transformation equation?

• Reflects the graph over the y-axis

• Reflects the graph over the x-axis

• Shifts the graph up

• Shifts the graph down

What is the effect of a negative 'K' in the transformation equation?

• Reflects the graph over the y-axis

• Reflects the graph over the x-axis

• Shifts the graph up

• Shifts the graph down

If H is negative, in which direction does the graph shift?

• Down

• Up

• Right

• Left

What is the effect of a positive 'H' in the transformation equation?

• Reflects the graph over the y-axis

• Reflects the graph over the x-axis

• Shifts the graph left

• Shifts the graph right