Power Functions and Their Properties

The video tutorial introduces power functions, explaining that a function is a power function if it can be expressed as K times x to the power of P. The tutorial covers identifying power functions, using algebraic rules to manipulate expressions, and understanding square roots as power functions. It provides examples of complex power functions and demonstrates algebraic transformations to express functions in the power function form.

What is a power function?

• A function that divides two variables

• A function that can be expressed as K times x to the power of P

• A function that multiplies two variables

• A function that adds two variables

What does it mean for a function to be proportional?

• The output is the difference between the input and a constant

• The output is equal to the input

• The output is a constant multiple of the input raised to a power

• The output is the sum of the input and a constant

How can you identify a power function from an equation?

• It has a variable in the exponent

• It can be written as a constant times a variable raised to a power

• It has a constant in the base

• It is a linear equation

What is the value of K in the function 5 over x to the third?

• -3

• 5

• 3

• 1

What is the value of P in the function 5 over x to the third?

• 5

• 1

• 3

• -3

Why is a function with a variable in the base not a power function?

• Because the exponent must be a constant

• Because the function must be quadratic

• Because the base must be a constant

• Because the function must be linear

How can you transform x to the negative 3 to identify it as a power function?

• By adding 3 to the exponent

• By multiplying by a constant

• By subtracting 3 from the exponent

• By rewriting it as 1 over x cubed

What is the equivalent of the square root of a number in terms of exponents?

• Raising the number to the power of 3

• Raising the number to the power of 1/2

• Raising the number to the power of 1

• Raising the number to the power of 2

What is the value of K in the function two-thirds x to the negative one?

• 3

• -1

• 2/3

• 1

What is the value of P in the function two-thirds x to the negative one?

• 2/3

• 3

• 1

• -1