Graphing 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 and discusses the relationship between the two functions, highlighting their inverse nature. The tutorial also covers the concepts of domain, range, and asymptotes for both functions, and shows their symmetry across the line y = x.

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

• 1

• 0

• 2

• 1/2

What does the exponential function y = 2^x approach as x becomes very large?

• -Infinity

• 0

• 1

• Infinity

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

• x = 0

• y = 0

• y = 1

• x = 1

In the function y = log base 2 of x, what is x when y = -1?

• 0

• 1

• 2

• 1/2

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

• y = 1

• x = 1

• y = 0

• x = 0

Which function has a domain of all real numbers?

• Neither

• Both

• y = log base 2 of x

• y = 2^x

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

• Negative numbers

• Positive numbers

• All real numbers

• Non-negative numbers

How are the exponential function y = 2^x and the logarithmic function y = log base 2 of x related?

• They are unrelated

• They are identical

• They are complements

• They are inverses of each other

Which line would show that the exponential and logarithmic functions are inverses?

• y = x

• x = y

• y = -x

• x = -y

What is the slope of the line that demonstrates the inverse relationship between the two functions?

• 1

• Undefined

• -1

• 0