Exploring Domain and Range Concepts

This video introduces the concept of functions, explaining their notation and graphing. It covers the difference between relations and functions, emphasizing the importance of each input having a single output. The video also delves into the concepts of domain and range, illustrating how to determine what values can be inputted into a function and what values can be expected as outputs. Examples are provided to clarify these concepts, including linear functions and quadratic functions.

What is the alternative notation for y = x^2 in function notation?

• f(x) = x^2

• f(x) = x + 2

• f(y) = x^2

• y = f(x^2)

What shape does the graph of y = x^2 resemble?

• A straight line

• A zigzag

• A circle

• A U-shape (parabola)

What happens to the graph of x^2 when you add 5 to it (x^2 + 5)?

• It does not change

• It shifts down by 5 units

• It becomes a straight line

• It shifts up by 5 units

What is a relation in the context of functions?

• A single input-output pair

• A graph of a function

• A mathematical equation

• A list of ordered pairs

What is the criterion for a relation to be considered a function?

• Every output has only one input

• Every input has only one output

• The equation is quadratic

• The graph is a straight line

Why is y = √x not considered a function?

• It is not a mathematical equation

• It has multiple outputs for a single input

• It has multiple inputs for a single output

• It has no outputs

What does the domain of a function represent?

• The equation of the function

• The list of all possible input values

• The list of all possible output values

• The shape of the graph

What is the domain of the function y = √x?

• All real numbers

• x ≤ 0

• x ≠ 0

• x ≥ 0

What is the range of the function y = x^2?

• All real numbers

• y ≥ 0

• y ≤ 0

• y ≠ 0

What is the range of the function y = √x - 7?

• y ≥ -7

• y = 0

• y ≠ -7

• y ≤ -7