Power Functions and Their Properties

This video tutorial covers power functions, focusing on their operations such as addition, subtraction, multiplication, and division. It explains how to handle exponents and like terms, and discusses domain considerations, including avoiding division by zero and imaginary numbers. The tutorial includes practice problems to reinforce understanding of these concepts.

What is the general form of a power function?

• y = a - X^b

• y = a + bX

• y = a * X^b

• y = a / X^b

Which of the following is a power function?

• f(x) = 2 - x

• f(x) = 2/x

• f(x) = 2x^2

• f(x) = 2x + 3

What is the result of adding f(x) = 2x^1/2 and g(x) = -6x^1/2?

• -8x^1/2

• 4x^1/2

• -4x^1/2

• 8x^1/2

When subtracting power functions, what happens to the negative sign?

• It becomes positive

• It remains negative

• It is ignored

• It doubles

How do you handle exponents when multiplying power functions?

• Subtract the exponents

• Add the exponents

• Divide the exponents

• Multiply the exponents

What is the simplified form of dividing f(x) = 2x^1/2 by g(x) = -6x^1/2?

• 3

• -3

• 1/3

• -1/3

What is the domain of a function?

• The set of output values

• The set of all real numbers

• The set of input values

• The range of y-values

Which condition must be avoided in the domain of a function?

• Multiplying by zero

• Dividing by zero

• Adding zero

• Subtracting zero

What is the domain of f(x) = 2x^1/2 + g(x) = -6x^1/2?

• x <= 0

• x > 0

• x >= 0

• x < 0

In the division of power functions, what must be checked for the domain?

• If neither is zero

• If both are zero

• If the denominator is zero

• If the numerator is zero