Understanding Functions, Domains, and Ranges

The video tutorial covers the basics of functions, including their domains and ranges. It uses real-world examples, such as Dustin's lawn mowing and Maria's tutoring charges, to illustrate how to define functions and determine their domains and ranges. The tutorial also explores abstract function definitions and analyzes the domain and range of quadratic and rational functions. Finally, it examines a function with a restricted domain to determine its range.

What is the domain of a function?

• The set of all possible outputs

• The set of all possible inputs

• The set of all negative numbers

• The set of all positive numbers

If Dustin charges $10 per hour for mowing lawns, what is the function for his charges?

• d(h) = 10 - h

• d(h) = h/10

• d(h) = 10 + h

• d(h) = 10h

What is the range of Dustin's charging function?

• Non-positive numbers

• All negative numbers

• All real numbers

• Non-negative rational numbers

Maria charges a minimum of $15 for tutoring. What is the domain of her function?

• All real numbers

• All integers

• Non-negative rational numbers

• All positive numbers

What is the range of Maria's charging function?

• All real numbers

• Rational numbers greater than or equal to $15

• All numbers less than $15

• All integers

For the function f(x) = 15x - 12, what is the domain?

• All negative numbers

• All integers

• All real numbers

• All positive numbers

For the function f(x) = 2x^2 + 5, what is the range?

• All integers

• All numbers less than 5

• All numbers greater than or equal to 5

• All real numbers

What is the domain of the function f(x) = 1/x?

• All positive numbers

• All negative numbers

• All real numbers except zero

• All real numbers

What is the range of the function f(x) = 1/x?

• All negative numbers

• All positive numbers

• All real numbers

• All real numbers except zero

In the restricted domain example, what is the range of the function y = x^2 - 5 for x in {-2, -1, 0, 1, 2}?

• {-5, -4, -1}

• {-1, -4, -5}

• {-2, -1, 0}

• {0, 1, 2}