Domain and Range of Functions

In this video, C chamber Jacob explains how to find the domain and range of the function f(x) = √(2 - x). The domain is determined by ensuring the expression under the square root is non-negative, resulting in x ≤ 2. The range is found by evaluating the smallest and largest possible values of the function, leading to f(x) ≥ 0. The video concludes with a brief mention of the next video in the series.

What is the function given in the video?

• f(x) = 2x

• f(x) = x^2 - 2

• f(x) = √(x - 2)

• f(x) = √(2 - x)

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

• By setting x > 2

• By setting x = 2

• By setting 2 - x = 0

• By setting 2 - x > 0

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

• They make the function zero.

• They make the function undefined.

• They result in a negative number under the square root.

• They result in a positive number under the square root.

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

• x > 2

• x < 2

• x ≤ 2

• x ≥ 2

What happens if you substitute x = 3 into f(x) = √(2 - x)?

• The function is negative.

• The function is positive.

• The function is undefined.

• The function is zero.

What is the smallest value of f(x) when x is in the domain?

• -1

• 1

• 0

• 2

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

• f(x) ≤ 0

• f(x) ≥ 0

• f(x) > 0

• f(x) < 0

If x = 1, what is the value of f(x) = √(2 - x)?

• 3

• 1

• 0

• 2

What is the value of f(x) when x = 0?

• 1

• 0

• 2

• 3

What is the key takeaway about the range of f(x) = √(2 - x)?

• It is limited to positive numbers only.

• It starts from zero and goes upwards.

• It includes negative numbers.

• It is undefined for all x.