Exponential and Logarithmic Functions Concepts

The video tutorial covers graphing exponential and logarithmic functions, focusing on transformations such as vertical stretches, compressions, shifts, and reflections. It explains how to identify key points and asymptotes for graphing. The tutorial includes examples of graphing both exponential and logarithmic functions, highlighting the inverse relationship between the two. Key concepts include understanding the base function, applying transformations, and determining domain and range.

What does the 'a' in the function f(x) = a * b^(x-h) + k represent?

• Base of the exponential function

• Horizontal shift

• Vertical stretch or compression

• Reflection over the y-axis

In the function f(x) = a * b^(x-h) + k, what does a negative 'h' indicate?

• Vertical compression

• Vertical stretch

• Shift to the right

• Shift to the left

What is the horizontal asymptote for the function f(x) = 3^(x-1) - 2?

• y = 0

• y = -2

• y = 1

• y = 2

How does a negative sign in front of the base affect the graph of an exponential function?

• It stretches the graph horizontally

• It shifts the graph up

• It reflects the graph over the x-axis

• It compresses the graph vertically

What is the range of the function f(x) = -2 * 2^x + 4?

• (0, 4)

• (4, ∞)

• (-∞, 4)

• (-∞, ∞)

What is the inverse relationship between exponential and logarithmic functions?

• They are reflections over the line y=x

• They have the same base

• They are reflections over the y-axis

• They have the same range

In logarithmic functions, what does the vertical asymptote represent?

• x = 1

• x = 0

• y = 0

• y = 1

What are the key points for the logarithmic function log base 3 of x?

• (1, 0) and (3, 1)

• (0, 0) and (1, 1)

• (0, 1) and (1, 3)

• (1, 1) and (3, 3)

How does a shift to the left affect the graph of a logarithmic function?

• It moves the vertical asymptote to the left

• It moves the horizontal asymptote to the left

• It compresses the graph horizontally

• It reflects the graph over the y-axis

What transformation occurs when a logarithmic function is shifted up?

• The graph is reflected over the x-axis

• The graph is compressed vertically

• The horizontal asymptote moves up

• The vertical asymptote moves up