Domain and Range of Functions

In this video, the instructor 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, leading to x ≤ 2. The range is found by evaluating the smallest and largest possible values of the function, resulting in f(x) ≥ 0. The video concludes with a brief mention of the next video in the series.

What is the function we are analyzing in this video?

• f(x) = 2x

• f(x) = x^2 - 2

• f(x) = √(2 - x)

• f(x) = √(x - 2)

To find the domain of f(x) = √(2 - x), what condition must be satisfied?

• 2 - x > 0

• 2 - x < 0

• 2 - x ≤ 0

• 2 - x ≥ 0

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

• x ≥ 2

• x ≤ 2

• x < 2

• x > 2

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

• It results in a negative number under the square root.

• It results in zero under the square root.

• It results in an imaginary number.

• It results in a positive number under the square root.

What happens if you try to calculate the square root of a negative number?

• You get an error.

• You get a zero.

• You get a complex number.

• You get a real number.

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

• -1

• 2

• 0

• 1

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)?

• 1

• 3

• 0

• 2

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

• 2

• 0

• 1

• 3

What should you do if you don't understand the domain and range concepts?

• Ignore them.

• Focus on the video explanation.

• Memorize the formulas.

• Skip to the next topic.