Determining Functions: Key Concepts and Applications

What is the first step in determining if an equation is a function?

• Isolate the x variable

• Check if the equation is linear

• Apply the horizontal line test

• Isolate the y variable

In a linear equation, what ensures that the equation is a function?

• Every x value maps to multiple y values

• Every y value maps to multiple x values

• Every x value maps to a unique y value

• The equation passes the horizontal line test

What happens when you introduce a square root while solving for y in a quadratic equation?

• It produces a unique solution for y

• It produces two different solutions for y

• It simplifies the equation

• It makes the equation linear

Why does a quadratic equation not represent a function?

• Because it produces multiple y values for a single x value

• Because it is not linear

• Because it has no solutions

• Because it fails the horizontal line test

What is the result of taking the cube root of a negative number?

• A positive number

• A negative number

• An imaginary number

• Zero

Why does y raised to an odd power produce a function?

• Because it has no solutions

• Because it produces a unique y value for each x value

• Because it is always negative

• Because it is always positive

What is the key difference between solving for y in quadratic and cubic equations?

• Neither produce unique solutions

• Both produce unique solutions

• Cubic equations produce unique solutions, quadratic do not

• Quadratic equations produce unique solutions, cubic do not

What does the absolute value of y represent?

• The distance of y from zero

• The reciprocal of y

• The square of y

• The cube of y

Why does an absolute value equation not represent a function?

• Because it is not linear

• Because it produces multiple y values for a single x value

• Because it has no solutions

• Because it fails the horizontal line test

What must be done to solve for y in an absolute value equation?

• Take the cube root

• Isolate the x variable

• Take the square root

• Create two separate equations