Understanding Logarithmic Functions

The video tutorial explains how to graph a logarithmic function, specifically y = log base 4 of x. It covers the domain, range, and vertical asymptote of the function, and demonstrates how to convert the logarithmic equation into its exponential form to calculate points for graphing. The tutorial also provides a step-by-step guide on plotting these points and interpreting the graph, emphasizing the importance of understanding the function's behavior and characteristics.

What is the domain of the function y = log base 4 of x?

• x = 0

• x < 0

• x > 0

• All real numbers

What is the range of the function y = log base 4 of x?

• x > 0

• x = 0

• x < 0

• All real numbers

What is the vertical asymptote of the function y = log base 4 of x?

• x = 0

• x = 4

• y = 4

• y = 0

How do you convert the logarithmic function y = log base 4 of x to its exponential form?

• 4^y = x

• y^4 = x

• x^4 = y

• 4^x = y

What is the horizontal intercept of the function y = log base 4 of x?

• (1, 0)

• (0, 4)

• (0, 1)

• (4, 0)

If y = 1, what is the corresponding x-value for the function y = log base 4 of x?

• x = 1

• x = 2

• x = 4

• x = 8

What is the x-value when y = 1.5 for the function y = log base 4 of x?

• x = 8

• x = 16

• x = 4

• x = 2

What is the x-value when y = 0.5 for the function y = log base 4 of x?

• x = 3

• x = 2

• x = 4

• x = 1

Which point is not on the given coordinate plane for the function y = log base 4 of x?

• (4, 1)

• (1, 0)

• (16, 2)

• (8, 1.5)

What does the graph of y = log base 4 of x approach as x approaches zero?

• The line x = 4

• The x-axis

• The y-axis

• The line y = x