Understanding Domain and Range of Functions

The video tutorial explains how to determine the domain and range of a function, focusing on a square root function. It covers solving inequalities to find the domain, expressing it in interval notation, and determining the range by analyzing the function's outputs. The tutorial also includes graphical verification of the domain and range.

What is the domain of a function?

• The set of all positive numbers

• The set of all negative numbers

• The set of all possible inputs

• The set of all possible outputs

Why must the radicand in a square root function be non-negative?

• To make the function continuous

• To ensure the function is linear

• To keep the function increasing

• To avoid complex numbers

What happens to the inequality sign when both sides are divided by a negative number?

• It remains the same

• It reverses direction

• It becomes undefined

• It becomes an equality

How is the domain expressed using interval notation for the function discussed?

• (-∞, 2]

• [2, ∞)

• (-∞, 2)

• [1, ∞)

What is the smallest possible value of the function discussed in the video?

• 0

• 1

• 2

• 3

How is the range of the function expressed using interval notation?

• [1, ∞)

• (1, ∞)

• (0, ∞)

• [0, ∞)

What is the rightmost point on the graph of the function?

• X = 0

• X = 1

• X = 2

• X = 3

What does projecting the graph onto the x-axis help determine?

• The intercept of the function

• The slope of the function

• The domain of the function

• The range of the function

What is the lowest point on the graph in terms of Y value?

• Y = 0

• Y = 3

• Y = 1

• Y = 2

What does projecting the graph onto the y-axis help determine?

• The intercept of the function

• The slope of the function

• The domain of the function

• The range of the function