Understanding Exponential and Logarithmic Functions

The video tutorial explains how to graph the exponential function y = 2^x and the logarithmic function y = log base 2 of x on the same coordinate plane. It demonstrates graphing by hand using a table of values, highlighting the exponential growth and horizontal asymptote of the exponential function, and the vertical asymptote of the logarithmic function. The tutorial also discusses the inverse relationship between the two functions, showing their symmetry across the line y = x.

What is the main goal of graphing the exponential and logarithmic functions together?

• To determine their maximum values

• To discuss their inverse relationship

• To compare their growth rates

• To find the intersection points

What is the y-value when x = 0 for the function y = 2^x?

• 4

• 2

• 1

• 0

Which point is the y-intercept of the exponential function y = 2^x?

• (1, 2)

• (1, 0)

• (0, 1)

• (0, 0)

What is the horizontal asymptote of the exponential function y = 2^x?

• x = 1

• y = 0

• x = 0

• y = 1

How is the logarithmic function y = log base 2 of x rewritten for easier graphing?

• As y = x^2

• As x = log base 2 of y

• As 2^y = x

• As y = 2^x

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

• y > 0

• x < 0

• y < 0

• x > 0

What is the vertical asymptote of the logarithmic function y = log base 2 of x?

• y = 1

• x = 1

• y = 0

• x = 0

How are the domains and ranges of the exponential and logarithmic functions related?

• They are identical

• They are inverses of each other

• They are unrelated

• They are both limited to positive values

What line demonstrates the symmetry of the exponential and logarithmic functions?

• y = 0

• x = y

• x = 0

• y = x

What does the symmetry across the line y = x indicate about the two functions?

• They are inverses

• They are identical

• They are parallel

• They are perpendicular