Understanding Exponential and Logarithmic Functions

This lesson by Bob Cappetta from the University of Illinois at Chicago covers graphing exponential and logarithmic functions. It begins with an introduction to exponential functions, explaining how to graph them and discussing their properties such as domain, range, and asymptotes. The lesson then explores inverse functions, particularly focusing on logarithms as inverses of exponential functions. It includes graphing techniques for logarithmic functions and discusses transformations such as shifts. The lesson concludes with a detailed analysis of graphing both exponential functions and their inverses, providing a comprehensive understanding of these mathematical concepts.

What is the horizontal asymptote of the function f(x) = 2^x?

• y = 0

• x = 0

• y = 1

• x = 1

Which of the following is the inverse of the function f(x) = 2^x?

• g(x) = x^2

• g(x) = log base 10 of x

• g(x) = 2^x

• g(x) = log base 2 of x

What is the vertical asymptote of the function g(x) = log base 2 of x?

• x = 0

• y = 0

• x = 1

• y = 1

How does shifting the graph of log base 2 of x by 3 units to the right and 2 units down affect its domain?

• Domain becomes x > 3

• Domain becomes x > 2

• Domain becomes x > 0

• Domain becomes x > 1

What is the vertical asymptote of the function y = 2 - log base 3 of (x - 1)?

• y = 1

• x = 0

• x = 1

• y = 0

For the function y = 2 - log base 3 of (x - 1), what is the domain?

• x > 2

• x > 0

• x > 3

• x > 1

What is the horizontal asymptote of the function f(x) = 3 + 2^(x-1)?

• x = 0

• y = 0

• x = 3

• y = 3

What is the range of the function f(x) = 3 + 2^(x-1)?

• y > 2

• y > 0

• y > 3

• y > 1

How do you find the inverse of the function f(x) = 3 + 2^(x-1)?

• Switch x and y, then solve for x

• Take the reciprocal of the function

• Square the function

• Switch x and y, then solve for y

What is the vertical asymptote of the inverse of f(x) = 3 + 2^(x-1)?

• x = 3

• y = 3

• x = 0

• y = 0