Graphing Exponential Functions through Transformations

Mr. Allen introduces graphing exponential functions, starting with the parent function and its domain and range. He then demonstrates transformations, including reflections and translations, and plots the transformed points. The video concludes with an analysis of the transformed graph, discussing intercepts and asymptotes.

What is the value of 2 to the power of 0?

• 4

• 2

• 1

• 0

What is the y-coordinate when x is 1 for the function f(x) = 2^x?

• 1

• 2

• 4

• 0.5

What is the equation of the asymptote for the parent function f(x) = 2^x?

• y = -1

• y = 0

• y = 2

• y = 1

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

• x > 0

• x ∈ ℝ

• x < 0

• x = 0

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

• y = 0

• y ∈ ℝ

• y > 0

• y < 0

What type of transformation does a negative sign in front of the function cause?

• Stretch

• Reflection

• Vertical shift

• Horizontal shift

What does the transformation x + 3 inside the function indicate?

• Shift left 3 units

• Shift right 3 units

• Shift down 3 units

• Shift up 3 units

What is the new y-coordinate after reflecting and shifting the point (0, 1) of the parent function?

• -1

• 1

• 2

• 0

What is the equation of the asymptote for the transformed function g(x)?

• y = -2

• y = 1

• y = 0

• y = 2

What is the range of the transformed function g(x)?

• y ∈ ℝ

• y = 2

• y < 2

• y > 2