Exploring Properties of Log and Exponential Functions

This lesson explores the graphs of exponential and logarithmic functions, focusing on their properties such as y-intercepts, asymptotes, and end behavior. It covers transformations like vertical reflection and translation, and examines the natural logarithm function as the inverse of the exponential function. Key points and domain and range are discussed to provide a comprehensive understanding of these mathematical concepts.

What is the y-intercept of the function f(x) = 2^x?

• (1, 1)

• (0, 0)

• (1, 0)

• (0, 1)

Which of the following is true about the asymptotes of the function g(x) = e^x?

• y = 0 is a horizontal asymptote

• x = 0 is a horizontal asymptote

• y = 0 is a vertical asymptote

• x = 0 is a vertical asymptote

What is the range of the function f(x) = 2^x?

• (0, ∞)

• (-∞, 0)

• (-∞, ∞)

• [0, ∞)

For the function g(x) = e^x, as x approaches negative infinity, g(x) approaches:

• 0

• -Infinity

• Infinity

• 1

What transformation is applied to h(x) if it includes a vertical flip?

• Multiplication by -1

• Addition of 3

• Subtraction of 3

• Division by -1

What is the new y-intercept after the transformation h(x) = -2^(x+3)?

• (0, -1)

• (0, 1)

• (0, 1/8)

• (0, -1/8)

What is the domain of the logarithmic function k(x) = ln(x)?

• (0, ∞)

• (-∞, 0)

• (-∞, ∞)

• [0, ∞)

Where is the vertical asymptote located in the function k(x) = ln(x)?

• x = 1

• y = 0

• y = 1

• x = 0

What is the x-intercept of the logarithmic function k(x) = ln(x)?

• (1, 0)

• (0, 1)

• (1, 1)

• (0, 0)

For the function k(x) = ln(x), as x approaches infinity, k(x) approaches:

• 0

• -Infinity

• 1

• Infinity