Exploring Domain and Range in Linear and Quadratic Functions

The video tutorial covers the concepts of domain and range, focusing on linear and quadratic functions. It explains the definitions of domain and range, provides problem-solving examples involving cost and uniforms, biking distance, and quadratic functions. The tutorial emphasizes identifying independent and dependent variables and using graphing calculators to analyze functions.

What is the domain of a function?

• The set of all dependent values

• The set of all independent values

• The set of all y-values

• The set of all z-values

In the context of domain and range, what does the term 'independent variable' refer to?

• The variable that depends on another variable

• The variable that is manipulated or controlled

• The variable that is constant

• The variable that is dependent

How can you remember the difference between domain and range?

• Domain comes after range alphabetically

• Range comes before domain alphabetically

• Domain comes before range alphabetically

• Range and domain are the same

In the function C = 3495U + 6.25, what does the variable U represent?

• The number of players

• The total price

• The number of uniforms

• The cost

In the function C = 3495U + 6.25, what does the variable C represent?

• The cost

• The total number

• The number of players

• The number of uniforms

If a student rides a bike for X minutes, what does the range represent in this context?

• The speed of the bike

• The distance in miles

• The time taken

• The number of minutes

For a quadratic function, what is typically the domain?

• All negative numbers

• All integers

• All positive numbers

• All real numbers

In the quadratic function x^2 - x - 6, what is the lowest y-value?

• -5.25

• -6.25

• -7.25

• -8.25

Which graph represents a function with a domain from -7 to 2?

• A graph with x-values from -2 to 7

• A graph with x-values from -4 to 1

• A graph with x-values from -7 to 2

• A graph with x-values from -3 to 2

What is the range of the function f(x) = 2x^2 + 3x when the domain is {-2, -1, 0}?

• {2, -1, 0}

• {2, 1, 0}

• {-2, -1, 0}

• {2, -1, 1}