Understanding Exponential and Logarithmic Functions

TLDR; Graph exponential and logarithmic functions on the same coordinate plane, analyze their properties, and understand their inverse relationship.

Graph the exponential function y = 2 raised to the power of x and determine corresponding y values for selected x values.

Plot the points on a coordinate plane and observe exponential growth due to the base being greater than 1.

Understand the domain (all real numbers) and the range (y is always greater than zero) of the exponential function.

Re-write the log function as an exponential function to complete a table of values by selecting y values and determining x.

Sketch the log function on a coordinate plane and observe the vertical asymptote at x = 0.

Note the domain (x greater than zero) and the range (all real numbers) of the logarithmic function.

Observe the interchanged x and y coordinates as well as the interchange of domain and range between the exponential and logarithmic functions.

Recognize that these two functions are inverses of one another and demonstrate their symmetry across the line y = x.

Understand that folding these two functions across the line y = x would match them perfectly, further indicating their inverse relationship.