Logarithmic Functions and Transformations

The video tutorial explains how to match logarithmic equations with their corresponding graphs. It covers the analysis of equations in the form of f(x) = log base a of x, where the function's behavior depends on the base value. The tutorial demonstrates graphing y = log base 1/2 of x and y = log base 4 of x using tables of values. It also explains how to reflect these graphs across the x-axis to obtain graphs of negative logarithmic functions.

What is the behavior of a logarithmic function when the base is greater than 1?

• The function is undefined.

• The function is increasing.

• The function is constant.

• The function is decreasing.

For the equation y = log base 1/2 of x, what is the nature of the graph?

• The graph is increasing.

• The graph is decreasing.

• The graph is a straight line.

• The graph is a parabola.

Which point is on the graph of y = log base 1/2 of x?

• (1, 2)

• (2, 1)

• (1, 0)

• (0, 1)

What is the equivalent exponential form of y = log base 4 of x?

• x^4 = y

• 4^x = y

• y^4 = x

• 4^y = x

Which point is on the graph of y = log base 4 of x?

• (4, 0)

• (0, 4)

• (1, 4)

• (4, 1)

How does the graph of y = -log base 1/2 of x differ from y = log base 1/2 of x?

• It is shifted upwards.

• It is reflected across the x-axis.

• It is reflected across the y-axis.

• It is shifted to the right.

Which point is on the graph of y = -log base 1/2 of x?

• (1, 2)

• (1, -2)

• (2, 1)

• (2, -1)

What transformation is applied to the graph of y = log base 4 of x to obtain y = -log base 4 of x?

• Translation upwards

• Reflection across the x-axis

• Reflection across the y-axis

• Translation downwards

Which point is on the graph of y = -log base 4 of x?

• (0, 4)

• (1, 4)

• (4, 1)

• (4, -1)

What happens to the y-coordinates of a graph when it is reflected across the x-axis?

• They remain the same.

• They become positive.

• They become negative.

• They are doubled.