Understanding Logarithmic Functions

The video tutorial explains how to graph the logarithmic equation y = log base 1/2 of x by hand. It begins by converting the logarithmic equation into its equivalent exponential form to create a table of values. The tutorial demonstrates selecting y-values to find corresponding x-values, plotting these points, and drawing the graph. It highlights the graph's behavior, including its vertical asymptote at x = 0. The video concludes with a discussion on the properties of logarithmic functions, emphasizing the conditions under which they increase or decrease.

What is the equivalent exponential form of the logarithmic equation y = log base 1/2 of x?

• 1/2^y = x

• x^1/2 = y

• x^y = 1/2

• 1/2^x = y

When graphing y = log base 1/2 of x, why do we select y values to find x values?

• Because x values are always negative

• Because the equation is in the form 1/2^y = x

• Because x values are always positive

• Because y values are easier to calculate

What is the x value when y = -1 for the equation 1/2^y = x?

• 2

• 1

• 4

• 1/2

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

• (0, 1)

• (2, -1)

• (1, 0)

• (1/2, 1)

What happens to the x values as y values increase in the graph of y = log base 1/2 of x?

• x values increase

• x values become negative

• x values remain constant

• x values decrease

What is the vertical asymptote of the graph of y = log base 1/2 of x?

• y = 1

• x = 1

• y = 0

• x = 0

What is the domain of the function y = log base 1/2 of x?

• (0, infinity)

• (1, infinity)

• (-infinity, 0)

• (-infinity, infinity)

What is the range of the function y = log base 1/2 of x?

• (0, infinity)

• (-infinity, 0)

• (-infinity, infinity)

• (1, infinity)

Why is the function y = log base 1/2 of x decreasing?

• Because x is always positive

• Because 1/2 is less than 1

• Because 1/2 is greater than 1

• Because y is always negative

What is the horizontal intercept of the function y = log base 1/2 of x?

• (1/2, 0)

• (0, 1)

• (0, 0)

• (1, 0)