Understanding Domains of Functions

The video tutorial explains how to determine the domain of different types of functions. It starts with a rational function, highlighting the need to avoid division by zero. Next, it covers square root functions, emphasizing the requirement for non-negative values under the radical. Finally, it discusses polynomial functions, which have no domain constraints, as they can accept any real number.

What is the domain of a function generally defined as?

• All possible values that make the function infinite

• All possible values that make the function zero

• All possible x-values that give a valid output

• All possible y-values of the function

For the function f(x) = (x + 5) / (x - 2), what value must x not be equal to?

• x = -5

• x = 0

• x = 5

• x = 2

Why must x not equal 2 in the function f(x) = (x + 5) / (x - 2)?

• It would make the function positive

• It would make the function negative

• It would make the denominator zero

• It would make the numerator zero

For the function g(x) = √(x - 7), what is the minimum value x can take?

• x = 14

• x = 0

• x = 7

• x = -7

Why must x be greater than or equal to 7 in the function g(x) = √(x - 7)?

• To ensure the function is always negative

• To ensure the function is always positive

• To avoid a zero value under the square root

• To avoid a negative value under the square root

What is the domain of the function h(x) = (x - 5)^2?

• All real numbers

• x = 5

• x < 5

• x > 5

Why does the function h(x) = (x - 5)^2 have a domain of all real numbers?

• Because squaring any real number results in a real number

• Because it has a denominator

• Because it involves a square root

• Because it is a linear function

What constraint is necessary for the domain of a function with a square root?

• The expression under the root must be non-negative

• The expression under the root must be zero

• The expression under the root must be negative

• The expression under the root must be positive

What happens if a denominator in a function equals zero?

• The function becomes zero

• The function becomes infinite

• The function becomes undefined

• The function becomes negative

Which type of function requires checking for negative values under a radical?

• Linear functions

• Square root functions

• Quadratic functions

• Rational functions