Understanding Exponential and Logarithmic Functions

The video tutorial introduces graphing log functions by first exploring exponential functions, specifically y = 2^x. It explains how to plot these functions and understand their properties, such as horizontal asymptotes. The tutorial then transitions to logarithmic functions, explaining their relationship as inverses to exponential functions. It demonstrates how to graph y = log base 2 of x by swapping x and y values from the exponential graph. The video also covers the domain and range of these functions, highlighting their inverse relationship. Finally, it provides guidance on a project involving log base 3 and log base 4 functions.

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

• 4

• 2

• 1

• 0

What happens to the base of an exponential function when the exponent is negative?

• It becomes zero

• It remains the same

• It becomes a fraction

• It doubles

How are the x and y values related in a logarithmic function compared to its exponential counterpart?

• They are multiplied

• They are added

• They are swapped

• They are subtracted

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

• All real numbers

• 0 to infinity

• Negative infinity to 0

• 1 to infinity

What is the range of the function y = 2^x?

• 0 to infinity

• Negative infinity to 0

• All real numbers

• 1 to infinity

What is the relationship between the domain of an exponential function and the range of its logarithmic inverse?

• They are doubled

• They are swapped

• They are unrelated

• They are identical

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

• 0 to infinity

• Negative infinity to positive infinity

• 1 to infinity

• Negative infinity to 0

How does the graph of a logarithmic function behave near the y-axis?

• It crosses the y-axis

• It moves away

• It hugs the y-axis

• It becomes horizontal

What is the first step in finding order pairs for log base 3 of x?

• Graph log base 3 directly

• Use y = 4^x to find pairs

• Use y = 3^x to find pairs

• Use y = 2^x to find pairs

What is the final step in finding order pairs for log base 4 of x?

• Use y = 2^x to find pairs

• Use y = 3^x to find pairs

• Use y = 4^x to find pairs

• Graph log base 4 directly