Transformations of Exponential and Logarithmic Functions

The video tutorial covers graphing exponential and logarithmic functions using transformations. It begins with an introduction to the parent functions and their characteristics, such as exponential growth and decay. The tutorial then explains transformation rules, including vertical and horizontal shifts, stretches, and reflections. It provides step-by-step examples of graphing exponential functions, highlighting key points and asymptotes. The video concludes with graphing logarithmic functions, emphasizing domain restrictions and transformations.

What is the key point that both exponential growth and decay graphs pass through?

• (0, 0)

• (1, 0)

• (0, 1)

• (1, 1)

What happens to the graph of an exponential function when the entire function is multiplied by a negative value?

• It shifts horizontally

• It reflects vertically

• It stretches vertically

• It shrinks horizontally

If you add a constant to the exponent in an exponential function, what type of transformation occurs?

• Horizontal shift

• Horizontal stretch

• Vertical shift

• Vertical stretch

In the function f(x) = -2^(x-1) + 2, what is the first transformation applied to the parent function 2^x?

• Horizontal reflection

• Vertical shift up

• Horizontal shift right

• Vertical reflection

For the function f(x) = 1/2^(-x-1) - 3, what is the final transformation applied?

• Vertical shift up

• Horizontal shift left

• Horizontal shift right

• Vertical shift down

What is the domain of the parent logarithmic function?

• All real numbers

• x > 0

• x < 0

• x ≠ 0

What type of asymptote does the parent logarithmic function have?

• Vertical at x = 1

• Horizontal at y = 1

• Vertical at x = 0

• Horizontal at y = 0

In the function f(x) = -log(2x + 4) + 2, what is the effect of the coefficient 2 in front of x?

• Vertical shrink

• Horizontal shrink

• Horizontal stretch

• Vertical stretch

What is the final transformation applied to the function f(x) = 2 * log(x - 1)?

• Vertical shift up

• Horizontal shift right

• Vertical stretch

• Horizontal stretch

In the function f(x) = log(x) - 1, what type of transformation is applied?

• Horizontal shift left

• Vertical stretch

• Vertical shift down

• Horizontal stretch