Understanding Exponential and Logarithmic Functions

The video tutorial explains how to match graphs to their corresponding equations, focusing on exponential and logarithmic functions. It covers the properties of exponential growth, the relationship between exponential and logarithmic functions, and how to identify inverse functions. The tutorial also discusses the graphical representation of these functions and their symmetry across the line y = x.

Which of the following functions represents exponential growth?

• y = 10^x

• y = x^2

• y = x^10

• y = log x

What is the base of the natural exponential function?

• 5

• 10

• e

• 2

Which graph increases faster, y = 10^x or y = e^x?

• Neither increases

• y = 10^x

• y = e^x

• Both increase at the same rate

If x = 1, what is the y-coordinate for the function y = e^x?

• 1

• 0

• 10

• e

What is the base of the common logarithm?

• 10

• 2

• e

• 5

Which of the following is an inverse function of y = 10^x?

• y = log x

• y = x^2

• y = x^10

• y = e^x

What point does the function y = log x pass through if y = 10^x passes through (1, 10)?

• (e, 1)

• (1, 10)

• (0, 0)

• (10, 1)

Which line do inverse functions reflect across?

• y = -x

• x = 0

• y = 0

• y = x

Which functions are symmetrical across the line y = x?

• y = 10^x and y = x^10

• y = log x and y = x^2

• y = e^x and y = natural log x

• y = x^2 and y = x^3

What is the relationship between y = e^x and y = natural log x?

• They are inverse functions

• They are both linear functions

• They are the same function

• They are unrelated