Understanding Power Functions

The video tutorial explains power functions, which are functions of the form f(x) = k * x^p, where p is any real number and k is a non-zero coefficient. It demonstrates how to identify power functions by analyzing given examples, including rewriting functions using exponent properties. The tutorial also highlights a function that is not a power function due to the addition of a constant term. Additionally, it covers converting radicals to power functions using rational exponents and provides examples and graphs of various power functions.

What is the general form of a power function?

• f(x) = k * x^p, where p is any real number and k is zero

• f(x) = k + x^p, where p is any real number and k is zero

• f(x) = k * x^p, where p is any real number and k is non-zero

• f(x) = k * x^p, where p is a positive integer and k is non-zero

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CCSS.HSA.APR.D.6

How can the function y = 1/x be rewritten as a power function?

• y = x^2

• y = x^0

• y = x^1

• y = x^-1

Which of the following is NOT a power function?

• y = x^0.5

• y = x^2 + 1

• y = 3x^2

• y = x^3

Why is y = x^2 + 1 not considered a power function?

• It is a linear function

• It is a radical expression

• It has a negative exponent

• It includes a constant term

How can the square root of x be expressed as a power function?

• x^2

• x^0.5

• x^1

• x^-1

What is the exponent when the square root of x is rewritten as a power function?

• 0.5

• 2

• 1

• -0.5

Which of the following is a power function?

• y = x^3

• y = x + 1

• y = 1/x

• y = x^2 + 1

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CCSS.HSF-IF.C.7A

What is the exponent in the power function y = 1/x?

• 1

• 2

• -1

• 0

Which function represents a power function with a negative exponent?

• y = x^0.5

• y = x^-2

• y = x^3

• y = x^2

What is a common characteristic of power functions?

• They are always linear functions

• They can be rewritten as radical expressions

• They always have a positive exponent

• They include additional terms like constants