Power Functions and Their Properties

The video tutorial explores power functions with fractional exponents, focusing on those with even and odd denominators. It explains the characteristics and graphing of these functions, including transformations such as reflections and translations. The tutorial also covers writing transformation functions and introduces the mathematical constant e, emphasizing its importance in exponential functions.

What is the form of the power functions discussed in the video?

• X to the power of a fractional number with numerator one

• X to the power of a whole number

• X to the power of a negative number

• X to the power of zero

What is the shape of the graph for power functions with even denominators?

• Exponential

• Linear

• Parabolic

• Square root shape

What is the domain of power functions with even denominators?

• Negative infinity to zero

• Zero to one

• Zero to infinity

• Negative infinity to infinity

What is the range of power functions with even denominators?

• Negative infinity to zero

• Negative infinity to infinity

• Zero to one

• Zero to infinity

What is the shape of the graph for power functions with odd denominators?

• Parabolic

• Exponential

• Linear

• Flattened S shape

What is the domain of power functions with odd denominators?

• Negative infinity to infinity

• Zero to one

• Zero to infinity

• Negative infinity to zero

What is the range of power functions with odd denominators?

• Negative infinity to infinity

• Zero to infinity

• Negative infinity to zero

• Zero to one

What transformation occurs when a negative sign is in front of the function with an even denominator?

• Vertical stretch

• Reflection over the x-axis

• Horizontal shift

• Reflection over the y-axis

What is the effect of adding a constant inside the function with an even denominator?

• Reflection over the x-axis

• Reflection over the y-axis

• Horizontal shift

• Vertical stretch

What transformation occurs when a negative sign is in front of the function with an odd denominator?

• Reflection over the x-axis

• Reflection over the y-axis

• Vertical stretch

• Horizontal shift