Understanding Logarithmic Functions

This video tutorial explains how to graph a logarithmic function, specifically y = log base 3 of x + 2. It covers the translation of the graph, determining the domain and range, and identifying the vertical asymptote. The tutorial also demonstrates how to graph the function by hand using an equivalent exponential equation and plotting points to sketch the graph accurately.

What is the domain of the function y = log base 3 of x + 2?

• All real numbers

• (0, ∞)

• [0, ∞)

• (-∞, ∞)

How does the graph of y = log base 3 of x + 2 differ from y = log base 3 of x?

• Shifted down by 2 units

• Shifted left by 2 units

• Shifted right by 2 units

• Shifted up by 2 units

What is the vertical asymptote of the function y = log base 3 of x + 2?

• x = 2

• x = 1

• x = 0

• x = -2

What is the equivalent exponential equation for y - 2 = log base 3 of x?

• x^(y-2) = 3

• 3^x = y - 2

• y = 3^(x-2)

• 3^(y-2) = x

If y = 3, what is the value of x in the equation 3^(y-2) = x?

• 1

• 3

• 9

• 27

What is the x-value when y = 4 in the equation 3^(y-2) = x?

• 3

• 12

• 6

• 9

What is the x-value when y = 1 in the equation 3^(y-2) = x?

• 1

• 1/3

• 9

• 3

Which point is not on the graph of y = log base 3 of x + 2?

• (2, 1)

• (9, 4)

• (3, 3)

• (1, 2)

What is the range of the function y = log base 3 of x + 2?

• (-∞, 0)

• [0, ∞)

• (-∞, ∞)

• (0, ∞)

What does the graph of y = log base 3 of x + 2 approach as x approaches 0?

• y-axis

• Line y = 2

• x-axis

• Line x = 2