Function Evaluation and Range Analysis

In this video tutorial, the instructor guides viewers through the process of finding the domain and range of a function, specifically f(x) = √(2 - x). The video begins with an introduction and objective, followed by a detailed explanation of how to determine the domain by ensuring the expression under the square root is non-negative. The instructor then explains how to find the range by evaluating the smallest and largest possible values of the function. The video concludes with a summary and a prompt to watch the next video in the series.

What is the main topic of the video?

• Graphing linear functions

• Solving quadratic equations

• Understanding imaginary numbers

• Finding the domain and range of a function

What is the function discussed in the video?

• f(x) = x^2 + 2

• f(x) = √(2 - x)

• f(x) = 2x - 3

• f(x) = x/2

How do you find the domain of f(x) = √(2 - x)?

• By setting x = 0

• By setting x^2 = 2

• By setting 2 - x = 0

• By setting 2 - x > 0

Why can't x be greater than 2 in the domain of f(x) = √(2 - x)?

• It results in a division by zero

• It makes the function undefined

• It results in a negative number under the square root

• It makes the function non-linear

What is the result of f(x) when x = 3?

• 0

• Imaginary number

• 2

• 1

What is the result of f(x) when x = 4?

• 0

• Imaginary number

• 2

• 1

What is the result of f(x) when x = 5?

• 2

• Imaginary number

• 1

• 0

What is the result of f(x) when x = 6?

• 0

• 2

• 1

• Imaginary number

What is the domain of the function f(x) = √(2 - x)?

• x > 2

• x < 2

• x ≤ 2

• x ≥ 2

What is the result of f(x) when x = -2?

• 4

• 1

• 0

• 2