Logarithmic Functions and Their Graphs

The video tutorial explores graphing various transformations of logarithmic functions, specifically focusing on log base 3. It begins with the basic graph of f(x) = log base 3 of x, identifying key features like x-intercepts and asymptotes. The tutorial then examines transformations such as scaling (log base 3 of x/3 and log base 3 of 3x), shifts (log base 3 of x-2), and reflections (log base 3 of -x). Each transformation's effect on the graph is analyzed, providing a comprehensive understanding of how these changes impact the function's behavior.

What is the primary purpose of plotting points when analyzing logarithmic functions?

• To determine the slope

• To identify the x-intercepts

• To find the y-intercepts

• To calculate the area under the curve

What is the x-intercept of the function f(x) = log base 3 of x?

• x = -1

• x = 3

• x = 1

• x = 0

How does the graph of f(x) = log base 3 of x behave as it approaches the y-axis?

• It diverges away from the y-axis

• It becomes parallel to the x-axis

• It becomes asymptotic to the y-axis

• It intersects the y-axis

How does the graph of f(x) = log base 3 of x behave as x approaches infinity?

• It decreases without bound

• It approaches a vertical asymptote

• It continues to increase without bound

• It approaches a horizontal asymptote

What is the primary characteristic of the graph of f(x) = log base 3 of x?

• It is asymptotic to the y-axis

• It is a straight line

• It is a parabola

• It is a circle

What is the x-intercept of the function f(x) = log base 3 of x?

• x = -1

• x = 3

• x = 1

• x = 0

How does the graph of f(x) = log base 3 of x behave as it approaches the y-axis?

• It diverges away from the y-axis

• It becomes asymptotic to the y-axis

• It intersects the y-axis

• It becomes parallel to the x-axis

How does the graph of f(x) = log base 3 of x behave as x approaches infinity?

• It approaches a vertical asymptote

• It approaches a horizontal asymptote

• It continues to increase without bound

• It decreases without bound

What is the primary characteristic of the graph of f(x) = log base 3 of x?

• It is a straight line

• It is a parabola

• It is asymptotic to the y-axis

• It is a circle

What happens to the graph of g(x) = log base 3 of (x/3) compared to f(x) = log base 3 of x?

• It compresses vertically

• It shifts downwards

• It stretches horizontally

• It shifts upwards