Domain and Intercepts of Radical Functions

The video tutorial explains how to analyze and graph two functions, f(x) = sqrt(4-x) and g(x) = sqrt(x-4). It covers determining the domain, horizontal and vertical intercepts, and sketching accurate graphs. For f(x), the domain is x ≤ 4, with a horizontal intercept at (4,0) and a vertical intercept at (0,2). For g(x), the domain is x ≥ 4, with a horizontal intercept at (4,0) and no vertical intercept. The video demonstrates graphing techniques and highlights differences in graph shapes.

What is the main task described in the introduction of the video?

• To learn about trigonometric functions

• To determine domain, intercepts, and sketch graphs

• To understand calculus concepts

• To solve quadratic equations

What is the domain of the function f(x) = √(4 - x)?

• x ≥ 4

• x > 4

• x < 4

• x ≤ 4

How do you find the horizontal intercept of f(x) = √(4 - x)?

• Set x to zero

• Set the expression under the radical to zero

• Set the derivative to zero

• Set the function equal to one

What is the horizontal intercept of f(x) = √(4 - x)?

• (0, 2)

• (2, 0)

• (4, 0)

• (0, 4)

How is the vertical intercept of f(x) = √(4 - x) determined?

• By setting x to zero

• By finding the derivative

• By setting the expression under the radical to zero

• By evaluating the function at x = 0

What is the vertical intercept of f(x) = √(4 - x)?

• (2, 0)

• (0, 4)

• (4, 0)

• (0, 2)

What is the purpose of using a graphing calculator in the video?

• To calculate derivatives

• To sketch the graph of the function

• To find intercepts

• To solve equations

What is the domain of the function g(x) = √(x - 4)?

• x < 4

• x ≥ 4

• x ≤ 4

• x > 4

How is the horizontal intercept of g(x) = √(x - 4) found?

• Set the derivative to zero

• Set the function equal to one

• Set the expression under the radical to zero

• Set x to zero

What is the horizontal intercept of g(x) = √(x - 4)?

• (4, 0)

• (2, 0)

• (0, 4)

• (0, 2)