Graphing and Transformations of Exponential Functions

This video tutorial covers graphing exponential functions with transformations, including scaling, translation, and reflection. It provides examples of how to apply these transformations to parent functions and determine domain, range, and horizontal asymptotes. The video also explains how to write equations for transformed functions and use properties of exponents to demonstrate graph equivalence.

What is the main focus of this video tutorial?

• Solving quadratic equations

• Understanding logarithmic functions

• Graphing linear functions

• Graphing exponential functions with transformations

Which of the following is true about the parent exponential function?

• It is always y = 1/3^x

• It is always y = 3^x

• It changes based on the given function

• It is always y = 2^x

What is the base of the parent function for y = 1/9 * 3^x?

• 3

• 1/9

• 9

• 1/3

What is the horizontal asymptote for the function y = 1/9 * 3^x?

• y = 3

• y = 0

• y = 1

• y = -1

In the function y = 2^(x+3) - 5, what transformation is applied to the x-value?

• Translation left by 3

• Translation right by 3

• Translation up by 5

• Translation down by 5

What is the range of the function y = 2^(x+3) - 5?

• (-∞, -5)

• (-∞, 5)

• (-5, ∞)

• (5, ∞)

What is the effect of the negative sign in y = -1 * (1/3)^x / 4?

• Reflection over the x-axis

• Reflection over the y-axis

• Horizontal stretch

• Vertical stretch

What is the domain of the function y = -1 * (1/3)^x / 4?

• (0, 1)

• (-∞, 0)

• (0, ∞)

• (-∞, ∞)

In the function y = 2^(-x) + 1, what does the -x indicate?

• Reflection over the x-axis

• Reflection over the y-axis

• Vertical translation

• Horizontal translation

What is the horizontal asymptote for y = 2^(-x) + 1?

• y = 2

• y = -1

• y = 1

• y = 0