Transformations and Properties of Logarithmic Functions

This video tutorial covers how to graph logarithmic functions through six examples, demonstrating two methods for graphing: using transformations and rewriting in exponential form. The tutorial explains the inverse relationship between logarithmic and exponential functions and provides detailed steps for graphing each example, including domain and range considerations. The video also explores transformations such as shifts, reflections, and stretches, offering multiple approaches to graphing logarithmic functions.

What is the relationship between logarithmic and exponential functions?

• They are the same.

• They are both linear functions.

• They are inverses of each other.

• They are unrelated.

How do you graph y = log base 3 of X using its inverse?

• Reflect it over the y-axis.

• Reflect it over the line y = x.

• Rotate it 90 degrees.

• Translate it upwards.

What transformation does a '+2' inside the logarithm function cause?

• Shift the graph right by 2.

• Shift the graph up by 2.

• Shift the graph left by 2.

• Shift the graph down by 2.

In the function y = log base 4 of X, what does a '-1' outside the logarithm do?

• Reflects the graph over the y-axis.

• Reflects the graph over the x-axis.

• Shifts the graph down by 1.

• Shifts the graph up by 1.

How do you find the domain of a logarithmic function?

• Set the argument not equal to zero.

• Set the argument equal to zero.

• Set the argument less than zero.

• Set the argument greater than zero.

What effect does a negative sign in front of the logarithm have on the graph?

• Shifts it left.

• Reflects it over the x-axis.

• Reflects it over the y-axis.

• Shifts it right.

In the function y = log base 5 of X, what does multiplying the function by 2 do?

• Shifts the graph down by 2.

• Shifts the graph up by 2.

• Stretches the graph vertically.

• Compresses the graph vertically.

What is the range of a logarithmic function?

• All positive numbers.

• All negative numbers.

• Numbers between 0 and 1.

• All real numbers.

How do you solve for x in a logarithmic equation?

• Exponentiate both sides.

• Divide both sides by the base.

• Multiply both sides by the base.

• Take the square root of both sides.

What does a vertical stretch by a factor of 3 do to the graph of a logarithmic function?

• Compresses it vertically.

• Stretches it vertically.

• Stretches it horizontally.

• Compresses it horizontally.