Graphing a logarithmic function with a horizontal shift

The video tutorial explains how to graph the function F(x) = log base 2 of (x + 3). It covers the basic properties of logarithmic functions, including their graphs and intercepts. The tutorial also discusses transformations, such as horizontal shifts, and how they affect the graph. By understanding these concepts, viewers can accurately graph logarithmic functions and identify key features like intercepts and shifts.

What is the base point that all logarithmic graphs pass through, regardless of the base?

• (0, 0)

• (1, 0)

• (1, 1)

• (0, 1)

Why do logarithmic graphs pass through the point (1, 0)?

• Because log base 10 of 1 is 0

• Because the base of the logarithm is always 1

• Because any number raised to the power of 0 is 1

• Because log base 2 of 0 is 1

What is the new x-intercept of the function F(x) = log base 2 of (x + 3)?

• (-2, 0)

• (-3, 0)

• (0, 0)

• (1, 0)

How does adding 3 to x in the function F(x) = log base 2 of (x + 3) affect the graph?

• It shifts the graph 3 units to the right

• It shifts the graph 3 units to the left

• It shifts the graph 3 units up

• It shifts the graph 3 units down

In the transformation of the graph, what does the term 'H' represent in the expression F(x) = log base a (x - H) + K?

• Amplitude

• Horizontal shift

• Vertical shift

• Frequency